{"messages": [{"content": "MF = 11. Let Z be the midpoint of segment FM. Point E is the reflection of point Z across point F. Let I be the rotation of point F by angle 11pi/12 around point Z. Line P is the perpendicular bisector of segment IE. Point G is the midpoint of segment MI. Let B be the midpoint of segment IZ. Let S be the rotation of point G by angle 3pi/4 around point B. Point O is the reflection of point S across line P. Point V is the midpoint of segment GM. Line U passes through point O parallel to line P. Let K be the perpendicular bisector of segment FV. Let N be the reflection of point V across point M. Let Y be the reflection of line K across line P. Lines U and Y intersect at point A. Point W is the midpoint of segment FN. Find the distance between points W and A. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.06", "dataset": "MATH"}
{"messages": [{"content": "HK = 6. Point L is the midpoint of segment KH. Let U be the perpendicular bisector of segment LH. Let Z be the midpoint of segment LH. Point M is the reflection of point Z across point H. Point X is the midpoint of segment LZ. Point W is the reflection of point X across line U. Find the distance between points M and W. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Let QN = 12. Point H is the midpoint of segment QN. Let T be the rotation of point H by angle pi/2 around point Q. Let Y be the angle bisector of angle TNQ. Point D is on line Y with |DN| = 9. Point E is the reflection of point N across segment TQ. Let L be the reflection of point D across point H. Let V be the reflection of point N across point L. What is the distance between points V and E? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.0", "dataset": "MATH"}
{"messages": [{"content": "BV = 3. Point S is the reflection of point V across point B. Let F be the rotation of point B by angle pi/2 around point S. Line R passes through point F perpendicular to segment FV. Point C is the reflection of point V across point S. Point H is the reflection of point C across line R. Let P be the midpoint of segment FV. Let J be the midpoint of segment BH. Find the distance between points P and J. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.42", "dataset": "MATH"}
{"messages": [{"content": "Let YI = 1. Let M be the midpoint of segment IY. Let J be the rotation of point M by angle 7pi/12 around point I. Point Z is the midpoint of segment JM. Let G be the reflection of point I across point Z. Point U is the midpoint of segment ZG. Point D is the midpoint of segment GM. Let B be the reflection of point U across point Z. What is the distance between points B and D? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.36", "dataset": "MATH"}
{"messages": [{"content": "HX = 11. Line N is the perpendicular bisector of segment XH. Line Y is the reflection of line N across point X. Point W is the midpoint of segment XH. Let T be the midpoint of segment XW. Point O is the reflection of point H across point T. Point J is the midpoint of segment XO. Point E is the reflection of point W across line Y. Find the distance between points E and J. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.75", "dataset": "MATH"}
{"messages": [{"content": "Let XC = 11. Let K be the line through points X and C. Point Y is on line K with |YX| = 1. Line E is the perpendicular bisector of segment CX. Point U lies on line E at distance 2 from point C. Let R be the midpoint of segment XY. Let S be the reflection of point U across point R. Point A is the midpoint of segment YU. Let H be the midpoint of segment SC. What is the length of segment AH? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Let AO = 7. Let Y be the reflection of point O across point A. Let G be the midpoint of segment AY. Point T is the reflection of point G across point O. Point Z is the midpoint of segment TY. Find the distance between points Y and Z. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.25", "dataset": "MATH"}
{"messages": [{"content": "Let MS = 6. Let R be the reflection of point S across point M. Let Q be the perpendicular bisector of segment RS. Point C is the reflection of point M across point S. Let B be the line through point C parallel to line Q. Let X be the reflection of point S across point C. Point L is obtained by rotating point S by angle 2pi/3 about point R. Let P be the reflection of point R across point X. Point Z is the reflection of point R across line B. Point H is the reflection of point P across segment LC. Find the distance between points H and Z. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.02", "dataset": "MATH"}
{"messages": [{"content": "MW = 11. Let Z be the midpoint of segment MW. Let R be the line through point M perpendicular to segment MW. Point N is on line R with |NZ| = 9. Point H is the reflection of point N across segment MW. Line A passes through point W perpendicular to segment HW. Point L is the reflection of point N across line A. Let U be the midpoint of segment HW. What is the length of segment LU? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.1", "dataset": "MATH"}
{"messages": [{"content": "BC = 5. Let E be the vector from point C to point B. Let L be the midpoint of segment CB. Point F is the translation of point L by vector E. Let Y be the perpendicular bisector of segment LF. Point X lies on line Y at distance 10 from point F. Point G is the midpoint of segment CL. Line N is the angle bisector of angle XLC. Let Q be the midpoint of segment XC. Point U is the midpoint of segment GQ. Let A be the midpoint of segment LU. Point S is the midpoint of segment GF. Point R is the reflection of point S across line N. Point P is the reflection of point R across segment AG. Find the distance between points A and P. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.07", "dataset": "MATH"}
{"messages": [{"content": "Let IG = 7. Let Z be the rotation of point I by angle 5pi/6 around point G. Line C passes through points Z and G. Line Y passes through points Z and I. Point A lies on segment IG. Point F is the reflection of point A across line Y. Point X is the reflection of point F across line C. Find the distance between points F and X. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.0", "dataset": "MATH"}
{"messages": [{"content": "IO = 5. Let U be the rotation of point O by angle 2pi/3 around point I. Let K be the midpoint of segment UI. Line A is the perpendicular bisector of segment OI. Point H is the reflection of point K across line A. Find the distance between points H and U. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.01", "dataset": "MATH"}
{"messages": [{"content": "JD = 7. Let C be the perpendicular bisector of segment DJ. Let V be the reflection of line C through point D. Point N is the reflection of point J across line V. Let Y be the midpoint of segment JD. What is the distance between points N and Y? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.5", "dataset": "MATH"}
{"messages": [{"content": "PY = 2. Point N is obtained by rotating point P by angle pi/2 about point Y. Point Q is obtained by rotating point Y by angle pi/12 about point P. Point E is the midpoint of segment QY. Line H passes through points N and Q. Line U passes through point E perpendicular to line H. Point R is the reflection of point Q across line U. What is the length of segment RP? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
{"messages": [{"content": "AT = 1. Point Z is obtained by rotating point A by angle 7pi/12 about point T. Point G is obtained by rotating point Z by angle 11pi/12 about point A. Point C is obtained by rotating point A by angle pi/6 about point T. Let U be the rotation of point G by angle pi/3 around point C. Let K be the rotation of point Z by angle 3pi/4 around point A. Point R is obtained by rotating point C by angle 7pi/12 about point A. Let J be the rotation of point T by angle pi/2 around point K. Let L be the rotation of point J by angle 5pi/6 around point A. Line W is the angle bisector of angle GLR. Let F be the line through point L perpendicular to line W. Let X be the reflection of point C across point U. Let S be the line through point K perpendicular to line F. Point O is the reflection of point X across line S. Point D is the reflection of point U across point L. Point N is the midpoint of segment DO. What is the distance between points N and U? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.19", "dataset": "MATH"}
{"messages": [{"content": "Let CR = 8. Point D is the reflection of point C across point R. Let Y be the rotation of point D by angle 3pi/4 around point C. Let H be the perpendicular bisector of segment CR. Line G is the reflection of line H across point R. Point W is the midpoint of segment RY. Point B is the midpoint of segment YD. Let N be the reflection of point W across point Y. Point T is the midpoint of segment CN. Point X is the reflection of point T across line G. Point J is the reflection of point X across segment CN. Find the length of segment BJ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41.3", "dataset": "MATH"}
{"messages": [{"content": "Let RN = 5. Point D is obtained by rotating point N by angle 5pi/6 about point R. Let H be the rotation of point D by angle 3pi/4 around point N. Let Z be the line through points D and H. Point P is the midpoint of segment DH. Let A be the reflection of line Z through point N. Line C passes through points P and R. Let Y be the reflection of point H across point R. Point X is the intersection of lines A and C. Find the length of segment YX. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28.73", "dataset": "MATH"}
{"messages": [{"content": "Let BL = 6. Point C is the midpoint of segment LB. Let J be the rotation of point B by angle 5pi/6 around point C. Point Q is obtained by rotating point C by angle 2pi/3 about point J. Point M is the reflection of point J across point L. Point S is the reflection of point Q across segment MB. Let W be the reflection of point C across point M. Find the distance between points W and S. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.65", "dataset": "MATH"}
{"messages": [{"content": "Let JZ = 7. Let Y be the reflection of point J across point Z. Let V be the midpoint of segment ZY. Let Q be the reflection of point Y across point J. Point N is the midpoint of segment VJ. Point A is the reflection of point N across point Q. What is the distance between points A and Q? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.25", "dataset": "MATH"}
{"messages": [{"content": "Let QJ = 4. Point G is the midpoint of segment JQ. Point S is the midpoint of segment GQ. Let N be the rotation of point J by angle 3pi/4 around point G. Point U is the midpoint of segment NS. Line C passes through points G and N. Point R is the reflection of point U across line C. Point X is the reflection of point R across segment QN. Find the distance between points X and Q. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.77", "dataset": "MATH"}
{"messages": [{"content": "XS = 1. Let J be the midpoint of segment SX. Point N is obtained by rotating point X by angle 5pi/6 about point J. Let C be the midpoint of segment JX. Let W be the midpoint of segment CN. Point G is the midpoint of segment SJ. Let K be the perpendicular bisector of segment JW. Let L be the midpoint of segment SN. Let R be the reflection of line K through point G. Line Q passes through point J parallel to line R. Point I is the reflection of point G across line Q. Find the distance between points L and I. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
{"messages": [{"content": "Let WV = 5. Let J be the perpendicular bisector of segment WV. Point U is the midpoint of segment VW. Let S be the reflection of point U across point V. Point A is the reflection of point S across line J. Point T is the midpoint of segment VS. Let O be the reflection of point A across point T. What is the distance between points U and O? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.5", "dataset": "MATH"}
{"messages": [{"content": "VN = 7. Point H is the midpoint of segment VN. Let B be the vector from point V to point H. Let P be the rotation of point N by angle pi/2 around point H. Let A be the midpoint of segment HV. Point Z is the translation of point N by vector B. Point R is the reflection of point A across point Z. Line Q passes through points P and H. Line I passes through point N perpendicular to line Q. Point W is the reflection of point N across segment VP. Let S be the line through point R perpendicular to line I. Line E passes through point H parallel to segment VP. Let X be the reflection of line E through point W. Line U is the reflection of line S across line Q. Point J is the midpoint of segment WA. Let Y be the line through point R parallel to line X. Lines Y and U intersect at point O. What is the distance between points J and O? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37.38", "dataset": "MATH"}
{"messages": [{"content": "UI = 2. Point E is obtained by rotating point I by angle pi/12 about point U. Let S be the vector from point U to point E. Point K is the reflection of point I across point E. Let J be the midpoint of segment IE. Let X be the reflection of point U across point E. Point Q is obtained by rotating point E by angle 5pi/6 about point U. Let Y be point Q translated by vector S. Let P be point J translated by vector S. Point W is the reflection of point Y across point E. Let V be the line through points Q and W. Point L is the reflection of point X across line V. Point N is the midpoint of segment KP. What is the length of segment LN? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.08", "dataset": "MATH"}
{"messages": [{"content": "AZ = 6. Point K is the reflection of point Z across point A. Let I be the line through points A and Z. Let C be the rotation of point K by angle pi/12 around point A. Line W passes through point C perpendicular to line I. Point Y is obtained by rotating point Z by angle pi about point C. Point L is the reflection of point Z across line W. Point U is obtained by rotating point Z by angle 5pi/12 about point L. Let V be the reflection of point Y across point K. Let B be the midpoint of segment VC. Let O be the midpoint of segment AU. Let S be the reflection of point B across point O. Find the distance between points B and S. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.04", "dataset": "MATH"}
{"messages": [{"content": "YA = 8. Let Q be the rotation of point A by angle 7pi/12 around point Y. Let G be the reflection of point Y across point A. Line H passes through points G and Y. Let F be the line through point Q parallel to line H. Point T is the reflection of point A across line F. Let P be the midpoint of segment QG. Find the distance between points T and P. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.64", "dataset": "MATH"}
{"messages": [{"content": "Let UQ = 4. Let Y be the reflection of point Q across point U. Line J is the angle bisector of angle QUY. Point O is obtained by rotating point Y by angle 7pi/12 about point U. Let X be the reflection of point O across point Y. Let B be the reflection of line J through point X. Line V is the perpendicular bisector of segment QO. Let L be the reflection of point X across point O. Line N passes through point Q parallel to line V. Let A be the vector from point O to point X. Lines B and N intersect at point C. Point E is the translation of point C by vector A. Point R is the reflection of point E across line B. Point T is the reflection of point E across point R. Line F passes through point T perpendicular to segment YL. Point H is the reflection of point C across line F. Find the distance between points U and H. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.09", "dataset": "MATH"}
{"messages": [{"content": "IU = 1. Line Z passes through points U and I. Line Q passes through point U perpendicular to line Z. Point L is the reflection of point U across point I. Point N is on line Q with |NU| = 5. Point G is the midpoint of segment LI. Line R passes through points N and L. Point S is the reflection of point G across line Q. Point T is the reflection of point S across line R. Point W is the midpoint of segment TI. What is the length of segment WS? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.43", "dataset": "MATH"}
{"messages": [{"content": "Let PS = 11. Let C be the reflection of point P across point S. Point U is obtained by rotating point C by angle 3pi/4 about point S. Point E is obtained by rotating point C by angle 5pi/12 about point P. Point A is the reflection of point P across point E. Line R is the perpendicular bisector of segment CS. Point X is the midpoint of segment CS. Let I be the midpoint of segment CX. Let Y be the perpendicular bisector of segment SU. Point O is obtained by rotating point A by angle pi/3 about point P. Point V is obtained by rotating point I by angle pi about point E. Let J be the reflection of point A across point P. Line G is the reflection of line Y across line R. Point L is the reflection of point V across segment OJ. Point N is the reflection of point L across line G. What is the distance between points N and E? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65.68", "dataset": "MATH"}
{"messages": [{"content": "OP = 3. Point K is the midpoint of segment OP. Let T be the midpoint of segment OK. Point V is the reflection of point T across point O. Line W is the perpendicular bisector of segment VK. Let A be the reflection of line W through point K. Point Q is the reflection of point O across line A. What is the distance between points Q and T? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.5", "dataset": "MATH"}
{"messages": [{"content": "OH = 9. Let A be the midpoint of segment HO. Line S is the perpendicular bisector of segment OA. P is constructed so that HP = 9. Let R be the line through point P parallel to line S. Let J be the rotation of point A by angle pi/6 around point H. Let N be the line through point O parallel to line R. Point T is the reflection of point J across segment HO. Point M is the midpoint of segment HJ. Let F be the line through point T parallel to line N. Point Q is the reflection of point M across segment HO. Point X is the midpoint of segment QJ. Segment HO and line F intersect at point Z. What is the measure of angle XZT, in radians? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.09", "dataset": "MATH"}
{"messages": [{"content": "Let JL = 4. Line O is the perpendicular bisector of segment JL. Let S be the vector from point J to point L. Let M be the midpoint of segment LJ. Point N is the translation of point L by vector S. Point P is the reflection of point N across line O. Point R is obtained by rotating point L by angle 11pi/12 about point N. Let X be the line through point P perpendicular to segment RM. Point H is the reflection of point M across line X. Let F be the midpoint of segment RM. Find the distance between points H and F. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.89", "dataset": "MATH"}
{"messages": [{"content": "BS = 7. Point F is the reflection of point B across point S. Let H be the rotation of point B by angle 3pi/4 around point S. Line M is the perpendicular bisector of segment BF. Let Y be the vector from point S to point B. Let L be the line through point H parallel to segment BF. Point T is obtained by rotating point B by angle 7pi/12 about point S. Let V be the reflection of point H across point F. Let W be the line through points T and V. Let P be point V translated by vector Y. Point D is the intersection of lines L and W. Point K is the reflection of point P across segment BF. Point J is the reflection of point K across point B. Point O is the reflection of point J across line M. Point A is the reflection of point D across point J. Find the length of segment AO. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52.03", "dataset": "MATH"}
{"messages": [{"content": "KW = 5. J is constructed so that WJ = 2. Let Z be the line through points J and W. Let R be the reflection of line Z through point K. Point P is the reflection of point J across line R. Point M is the reflection of point W across segment PK. What is the length of segment MK? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.0", "dataset": "MATH"}
{"messages": [{"content": "Let SI = 4. Let E be the rotation of point S by angle pi/6 around point I. Let G be the angle bisector of angle IES. Point C is the reflection of point S across line G. Point J is the reflection of point C across segment SI. What is the length of segment JC? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.93", "dataset": "MATH"}
{"messages": [{"content": "Let BY = 11. Let X be the midpoint of segment YB. Let E be the midpoint of segment BX. Let R be the midpoint of segment XE. Let J be the reflection of point B across point R. Point Z is obtained by rotating point R by angle 7pi/12 about point E. Line V is the angle bisector of angle XZB. Let L be the line through point B parallel to line V. Let D be the line through point R parallel to line L. Let F be the reflection of line D across line L. Line A is the reflection of line D across line V. Line N passes through points Z and J. Point Q is the intersection of lines F and N. Point W is the reflection of point Q across line A. Find the length of segment QW. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.84", "dataset": "MATH"}
{"messages": [{"content": "WE = 12. Let G be the reflection of point W across point E. Let B be the vector from point E to point G. Point S is the translation of point G by vector B. Point C is obtained by rotating point S by angle 5pi/12 about point W. Let J be the perpendicular bisector of segment GW. Let I be the reflection of line J through point S. Point M is the reflection of point E across point C. Point Y is the reflection of point S across line I. Find the distance between points Y and M. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104.03", "dataset": "MATH"}
{"messages": [{"content": "Let NO = 10. Let Y be the rotation of point N by angle pi/4 around point O. Let H be the reflection of point Y across point N. Let E be the perpendicular bisector of segment OY. Point F is the reflection of point N across line E. Point J is the midpoint of segment FH. Let B be the midpoint of segment JO. What is the length of segment BY? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.79", "dataset": "MATH"}
{"messages": [{"content": "UP = 8. Point M is the reflection of point U across point P. Line H passes through point M perpendicular to segment UM. Point T is the reflection of point P across line H. Let W be the midpoint of segment UP. Find the distance between points W and T. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.0", "dataset": "MATH"}
{"messages": [{"content": "Let LZ = 2. Point O is obtained by rotating point Z by angle pi about point L. Point U is obtained by rotating point L by angle pi/2 about point Z. Point K is the midpoint of segment UZ. Line G is the perpendicular bisector of segment OU. Point X lies on segment ZL. Let F be the perpendicular bisector of segment UZ. Line W is the reflection of line G across line F. Line I is the reflection of line F across line G. Lines I and W intersect at point H. Let R be the line through point U parallel to line W. Let P be the reflection of line F through point X. Point N is the intersection of lines P and R. Point M is the reflection of point K across point H. What is the distance between points M and N? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.2", "dataset": "MATH"}
{"messages": [{"content": "XT = 2. Let A be the vector from point T to point X. Let P be the midpoint of segment XT. Point S is the translation of point X by vector A. Point W is obtained by rotating point P by angle pi/3 about point S. Let G be the line through points T and X. Let H be the line through point S perpendicular to line G. Point E is obtained by rotating point W by angle 5pi/12 about point S. Let R be the perpendicular bisector of segment WP. Point F is obtained by rotating point E by angle pi/3 about point S. Point I is the reflection of point E across segment FT. Let Q be the midpoint of segment FT. Point D is the reflection of point Q across line H. Point Z is the reflection of point D across line R. What is the distance between points I and Z? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.27", "dataset": "MATH"}
{"messages": [{"content": "Let KV = 11. Point N is obtained by rotating point K by angle 5pi/6 about point V. Let G be the perpendicular bisector of segment VN. Line H passes through point N parallel to line G. Let P be the line through point K perpendicular to line H. Let J be the line through point V perpendicular to line P. Point D is the reflection of point N across line J. What is the distance between points D and N? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.0", "dataset": "MATH"}
{"messages": [{"content": "SD = 2. Let E be the midpoint of segment SD. Let R be the perpendicular bisector of segment SD. Let K be the midpoint of segment SE. Point T is the reflection of point D across point S. Let U be the midpoint of segment KE. Point F is the midpoint of segment TE. Point H is the reflection of point U across line R. Let I be the midpoint of segment EU. Point V is the midpoint of segment ED. Point L is obtained by rotating point V by angle 7pi/12 about point U. Let J be the rotation of point I by angle 11pi/12 around point T. Point Y is obtained by rotating point K by angle pi/12 about point J. Let X be the reflection of point Y across point H. Let A be the midpoint of segment LX. Point Z is the reflection of point F across segment LX. What is the distance between points A and Z? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "SD = 4. Point A is obtained by rotating point D by angle 7pi/12 about point S. Point Q is the midpoint of segment AD. Point X is the reflection of point S across point Q. Line Y is the angle bisector of angle XQD. Point M is the reflection of point D across line Y. What is the length of segment MQ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.17", "dataset": "MATH"}
{"messages": [{"content": "Let WU = 7. Let G be the perpendicular bisector of segment UW. Point R lies on line G at distance 3 from point U. Point H is the reflection of point R across point U. Point Q is the midpoint of segment UW. Let X be the perpendicular bisector of segment QR. Line P is the reflection of line X across point Q. Line T passes through point W parallel to line P. Line L is the reflection of line T across line X. Point K is the reflection of point U across segment QH. Point E is the reflection of point H across line L. Find the distance between points K and E. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.41", "dataset": "MATH"}
{"messages": [{"content": "FB = 7. Let E be the rotation of point F by angle 5pi/6 around point B. Let P be the rotation of point B by angle 3pi/4 around point E. Let U be the rotation of point F by angle pi/6 around point E. Let A be the reflection of point F across point P. Point N is the midpoint of segment FU. Let L be the midpoint of segment AN. Let J be the reflection of point L across point F. What is the distance between points J and L? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38.24", "dataset": "MATH"}
{"messages": [{"content": "Let EB = 10. Let Z be the rotation of point B by angle pi/6 around point E. Let O be the reflection of point B across point E. Let H be the reflection of point O across point Z. Point C is the reflection of point E across point H. Let A be the vector from point O to point Z. Let U be the perpendicular bisector of segment ZO. Let Q be point B translated by vector A. Point M is obtained by rotating point Z by angle 3pi/4 about point H. Line D passes through point M parallel to line U. Let R be the midpoint of segment HZ. Line G passes through point C perpendicular to segment HZ. Point F is the reflection of point R across line G. Line D and segment CQ intersect at point K. Find the distance between points F and K. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53.98", "dataset": "MATH"}
{"messages": [{"content": "Let XQ = 6. Point P is obtained by rotating point X by angle 7pi/12 about point Q. Let Z be the perpendicular bisector of segment QX. Line H passes through point P perpendicular to line Z. Point N is the reflection of point P across line Z. Point A is the midpoint of segment QN. Point S is the reflection of point A across line H. Let O be the reflection of point A across point S. Point W is the reflection of point O across line Z. Let D be the midpoint of segment WA. Find the distance between points D and X. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.2", "dataset": "MATH"}
{"messages": [{"content": "Let ZC = 5. Let J be the midpoint of segment ZC. Line F is the perpendicular bisector of segment ZC. Let N be the rotation of point Z by angle pi/12 around point C. Point M is the reflection of point J across point N. Let D be the line through point C parallel to line F. Let G be the angle bisector of angle ZMN. Point S is the reflection of point N across segment ZC. Let I be the line through point Z parallel to line G. Lines I and D intersect at point H. Let Q be the midpoint of segment SZ. Let E be the midpoint of segment QJ. Find the length of segment HE. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.32", "dataset": "MATH"}
{"messages": [{"content": "Let GI = 10. Line N passes through points I and G. Let A be the perpendicular bisector of segment IG. Let X be the vector from point G to point I. Point Z is obtained by rotating point I by angle pi/4 about point G. Let P be the reflection of line A through point I. Let Y be point Z translated by vector X. Let H be the reflection of point G across point Y. Let Q be point H translated by vector X. Let F be the rotation of point Q by angle 5pi/12 around point G. Let V be the rotation of point H by angle 2pi/3 around point Z. Let U be the midpoint of segment FV. Let W be the line through point H parallel to line N. Point T is the intersection of lines P and W. Point B is the reflection of point Q across segment UF. What is the distance between points T and B? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87.54", "dataset": "MATH"}
{"messages": [{"content": "Let KP = 12. Let X be the vector from point P to point K. Let I be the rotation of point K by angle 3pi/4 around point P. Line W passes through points K and I. Line M passes through points K and P. Point J is the reflection of point I across point K. Point D is the translation of point K by vector X. Let G be the line through points D and J. Line R is the reflection of line G across line W. Point F is the reflection of point J across line M. Point H is the reflection of point I across line R. Let B be the midpoint of segment FH. Point A is the reflection of point B across line G. What is the distance between points A and K? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.74", "dataset": "MATH"}
{"messages": [{"content": "Let BF = 11. Line A is the perpendicular bisector of segment BF. Let J be the line through point F parallel to line A. Let O be the reflection of point F across point B. Let V be the rotation of point B by angle 5pi/6 around point O. Let U be the reflection of point B across point O. Point R is obtained by rotating point U by angle pi/6 about point O. Let C be the midpoint of segment RU. Point I is the reflection of point B across line J. Let H be the midpoint of segment BV. Line J and segment IC intersect at point K. What is the length of segment HK? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.54", "dataset": "MATH"}
{"messages": [{"content": "Let MT = 10. Point L is the reflection of point T across point M. Let N be the perpendicular bisector of segment ML. Let X be the perpendicular bisector of segment MT. Point W is the midpoint of segment MT. Point O is the reflection of point T across line N. Point U is on line X with |UO| = 3. Let J be the midpoint of segment MU. Let V be the midpoint of segment OU. Line D is the perpendicular bisector of segment WM. Point P is the reflection of point V across line D. Let Q be the reflection of point W across point J. What is the distance between points P and Q? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.59", "dataset": "MATH"}
{"messages": [{"content": "BV = 7. Point Z is the midpoint of segment BV. Let N be the rotation of point B by angle 2pi/3 around point Z. Let E be the vector from point B to point V. Line J passes through points V and N. Let I be point V translated by vector E. Line Y passes through point V perpendicular to line J. Point O is on line Y with |ON| = 8. Point D is the reflection of point I across point O. Point X is the midpoint of segment OB. Let C be the reflection of point N across point X. Point Q is the midpoint of segment BD. What is the distance between points C and Q? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Let AX = 4. Let Q be the rotation of point A by angle pi/6 around point X. Point F is the reflection of point X across point A. Point G is the reflection of point Q across point X. Let H be the reflection of point G across point F. Point D is the midpoint of segment XQ. Point W is the midpoint of segment FQ. Point K is the midpoint of segment WX. Let V be the midpoint of segment KA. Let E be the reflection of point H across point D. Let R be the reflection of point E across point W. Find the distance between points R and V. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.09", "dataset": "MATH"}
{"messages": [{"content": "Let VM = 7. Let S be the midpoint of segment VM. Line J passes through points S and M. Let R be the line through point V perpendicular to line J. Point N is the reflection of point M across line R. Find the distance between points N and V. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.0", "dataset": "MATH"}
{"messages": [{"content": "TZ = 10. Let Y be the rotation of point T by angle 11pi/12 around point Z. Let F be the midpoint of segment TZ. Line B is the perpendicular bisector of segment TF. Point H is on line B with |HZ| = 10. Point S is the reflection of point Y across line B. Point W is the midpoint of segment YS. Point Q is the reflection of point Y across segment TZ. Let N be the line through point H parallel to segment TZ. Point O is the reflection of point W across line N. Find the length of segment OQ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26.35", "dataset": "MATH"}
{"messages": [{"content": "TH = 7. Let W be the perpendicular bisector of segment HT. Line Q is the reflection of line W across point T. Let U be the reflection of point H across point T. Line A is the reflection of line Q across line W. Point S lies on line A at distance 10 from point T. Point Y is the midpoint of segment SU. Line L passes through points Y and H. Let D be the reflection of line W across line L. Point F is the intersection of line D and segment TS. Point V is the reflection of point S across line L. What is the distance between points V and F? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.67", "dataset": "MATH"}
{"messages": [{"content": "DK = 4. P is constructed so that KP = 2. Point J is obtained by rotating point P by angle 5pi/12 about point K. Point E is the reflection of point P across point K. Point F is the reflection of point J across point P. Point Q is the reflection of point F across segment EK. Find the distance between points E and Q. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.81", "dataset": "MATH"}
{"messages": [{"content": "Let RK = 9. Let M be the rotation of point K by angle pi/2 around point R. Let O be the rotation of point R by angle pi/4 around point M. Point J is the midpoint of segment KR. Let D be the midpoint of segment KO. Point C is the reflection of point J across point D. What is the length of segment CJ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.89", "dataset": "MATH"}
{"messages": [{"content": "WA = 3. Let B be the reflection of point A across point W. Let R be the reflection of point A across point B. Let U be the line through point B perpendicular to segment AW. Let D be the reflection of line U through point R. Point P is on line U. Point O is the reflection of point P across line D. What is the distance between points O and P? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.0", "dataset": "MATH"}
{"messages": [{"content": "MN = 8. Let H be the line through points M and N. Line J passes through point M perpendicular to line H. Let U be the rotation of point M by angle pi/12 around point N. Point G is obtained by rotating point U by angle pi/4 about point M. Let V be the vector from point U to point N. Let R be the line through point G parallel to line J. Point C is the translation of point G by vector V. Let F be the rotation of point M by angle 11pi/12 around point N. Point W is obtained by rotating point F by angle 5pi/12 about point C. Point D is the reflection of point U across point W. Point I is the reflection of point D across line R. Point O is the reflection of point C across point M. Point A is the reflection of point W across point I. What is the length of segment OA? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57.45", "dataset": "MATH"}
{"messages": [{"content": "Let MS = 12. Let C be the perpendicular bisector of segment SM. Line J passes through point M parallel to line C. Point Y is obtained by rotating point S by angle pi about point M. Let G be the reflection of line J through point S. Let I be the midpoint of segment MY. Point W is the reflection of point I across line G. Let P be the reflection of point I across point W. Find the distance between points I and P. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120.0", "dataset": "MATH"}
{"messages": [{"content": "QV = 1. Let G be the line through points Q and V. Point B is on line G with |BV| = 7. Point E is obtained by rotating point V by angle pi/3 about point Q. Line A is the perpendicular bisector of segment VQ. Line X is the perpendicular bisector of segment EQ. Line T passes through point Q parallel to line X. Let Y be the reflection of point B across point E. Point W is the reflection of point Y across line T. Point P is the reflection of point W across line A. Find the measure of angle YWP, in radians. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.09", "dataset": "MATH"}
{"messages": [{"content": "BE = 4. Point G is the reflection of point B across point E. Let A be the rotation of point E by angle 11pi/12 around point B. Let N be the midpoint of segment BA. Let U be the midpoint of segment GN. Point L is the midpoint of segment AU. What is the length of segment NL? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.52", "dataset": "MATH"}
{"messages": [{"content": "Let ZU = 1. Point Q is the reflection of point U across point Z. Point S is obtained by rotating point Z by angle pi/12 about point Q. Point L is the reflection of point S across segment UZ. Let I be the midpoint of segment UZ. Let K be the midpoint of segment IL. Let N be the reflection of point K across point S. What is the distance between points Z and N? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
{"messages": [{"content": "Let WI = 9. Point M is obtained by rotating point I by angle 3pi/4 about point W. Let G be the angle bisector of angle WMI. Line D passes through point I parallel to line G. Point E is obtained by rotating point I by angle 7pi/12 about point W. Line Z is the reflection of line D across line G. Let X be the midpoint of segment IM. Let O be the rotation of point E by angle 7pi/12 around point X. Point J is the reflection of point E across line Z. Point Y is the reflection of point J across segment IM. Let V be the midpoint of segment OI. Let L be the midpoint of segment MV. Find the length of segment LY. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.7", "dataset": "MATH"}
{"messages": [{"content": "Let CK = 5. Point O is the reflection of point K across point C. Let Z be the perpendicular bisector of segment OK. Line M passes through point O parallel to line Z. Point R is the reflection of point C across line M. Point V is the reflection of point R across line Z. Point I is the midpoint of segment OC. Let N be the reflection of point V across point I. Point W is the reflection of point N across point V. Point A is the midpoint of segment OW. Point E is the reflection of point V across point A. What is the distance between points C and E? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.0", "dataset": "MATH"}
{"messages": [{"content": "Let AB = 1. Let AD = 4. Point N is obtained by rotating point A by angle 5pi/6 about point D. Line G is the perpendicular bisector of segment DN. Let H be the line through point B parallel to line G. Point P is on line H. Point J is the reflection of point D across point N. Let S be the reflection of line G through point P. Point O lies on line S. Point Z is the reflection of point D across segment OJ. Find the distance between points J and Z. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.0", "dataset": "MATH"}
{"messages": [{"content": "Let NM = 12. Line O passes through points N and M. Let A be the line through point M perpendicular to line O. Let Z be the rotation of point N by angle 7pi/12 around point M. Let F be the reflection of line A through point Z. Let L be the line through point Z parallel to line F. Point B is the reflection of point M across line L. Let Q be the reflection of point B across point Z. Point G is the reflection of point Q across point N. Find the distance between points Z and G. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44.09", "dataset": "MATH"}
{"messages": [{"content": "Let PR = 10. Let Q be the reflection of point P across point R. Let Z be the rotation of point P by angle 5pi/6 around point Q. Let U be the midpoint of segment ZQ. Let O be the line through points Q and U. Point C is the reflection of point R across point Q. Point X is on line O. Point F is the reflection of point R across point X. Point G is the midpoint of segment CF. Find the measure of angle UXG, in radians. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.52", "dataset": "MATH"}
{"messages": [{"content": "Let IZ = 12. Point R is the reflection of point Z across point I. Point M is the reflection of point R across point Z. Point O is the midpoint of segment ZI. Point C is the midpoint of segment MO. Find the distance between points C and R. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33.0", "dataset": "MATH"}
{"messages": [{"content": "Let NA = 1. Let K be the rotation of point A by angle 11pi/12 around point N. Point V is the midpoint of segment NK. Let U be the midpoint of segment VK. Point P is the reflection of point U across segment KA. What is the length of segment PK? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "RL = 7. Line K is the perpendicular bisector of segment RL. Line J passes through point R parallel to line K. Let N be the reflection of point L across point R. Let A be the reflection of line J across line K. Let D be the line through point N parallel to line K. Point G is on line D with |GR| = 11. Let P be the reflection of point L across point G. Point U is the reflection of point P across line A. Let H be the reflection of point N across point U. Let Z be the reflection of point H across point N. Find the distance between points H and Z. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "189.65", "dataset": "MATH"}
{"messages": [{"content": "Let IH = 3. Let W be the midpoint of segment HI. Let L be the reflection of point W across point H. Point O is obtained by rotating point W by angle 7pi/12 about point I. Let P be the angle bisector of angle OIH. Point Q is the reflection of point H across line P. Point F is the reflection of point Q across segment OW. What is the length of segment FL? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.55", "dataset": "MATH"}
{"messages": [{"content": "JP = 4. Line Y is the perpendicular bisector of segment PJ. Let E be the midpoint of segment JP. Let H be the midpoint of segment EP. Let M be the midpoint of segment HE. Point B is obtained by rotating point E by angle 2pi/3 about point M. Point G is the reflection of point M across line Y. Point V is the reflection of point B across segment HE. Point S is the reflection of point H across segment GV. Point X is the midpoint of segment GV. What is the distance between points S and X? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Let JA = 9. Let F be the rotation of point J by angle 2pi/3 around point A. Line Z is the angle bisector of angle FAJ. Let Q be the line through point J parallel to line Z. Let C be the midpoint of segment AF. Point O is the reflection of point C across point J. Let P be the reflection of point O across point F. Point G is the reflection of point P across line Q. Find the distance between points G and O. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31.5", "dataset": "MATH"}
{"messages": [{"content": "ZA = 9. Let N be the midpoint of segment AZ. Let E be the reflection of point N across point A. Point B is the midpoint of segment ZN. Point F is obtained by rotating point A by angle pi/6 about point E. Point P is the midpoint of segment BF. Let T be the line through points P and Z. Line S passes through point E parallel to line T. Point U is the reflection of point Z across line S. Find the length of segment UZ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.04", "dataset": "MATH"}
{"messages": [{"content": "Let PD = 10. Point I is the reflection of point D across point P. Let F be the rotation of point P by angle pi/12 around point I. Line N is the angle bisector of angle FDP. Line Z passes through point D perpendicular to line N. Point V is the reflection of point I across line N. Line E passes through points I and P. Let C be the vector from point I to point D. Point U is the translation of point F by vector C. Point A is the reflection of point U across line Z. Let G be the line through point A perpendicular to line N. Point J is obtained by rotating point P by angle 3pi/4 about point F. Point K is the midpoint of segment JU. Let R be the midpoint of segment KJ. Let L be the reflection of point D across point I. Point O is the reflection of point A across segment VR. Let M be the line through point O perpendicular to line E. Line H is the reflection of line M across line G. Line H and segment VR intersect at point T. Find the length of segment TL. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31.49", "dataset": "MATH"}
{"messages": [{"content": "IJ = 4. Let F be the vector from point I to point J. Let Q be point J translated by vector F. Let U be the rotation of point J by angle 3pi/4 around point Q. Let T be the reflection of point Q across point I. Let E be the rotation of point Q by angle pi/6 around point I. Let P be the rotation of point E by angle pi/2 around point J. Let R be the reflection of point U across point Q. Point C is the midpoint of segment PT. Point B is the reflection of point U across segment RC. Point V is the reflection of point B across segment UE. Point W is the reflection of point V across segment RC. What is the distance between points E and W? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.05", "dataset": "MATH"}
{"messages": [{"content": "DU = 12. Point H is obtained by rotating point D by angle 5pi/12 about point U. Let A be the midpoint of segment DH. Let I be the midpoint of segment AD. Point E is the midpoint of segment UI. Find the distance between points A and E. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.1", "dataset": "MATH"}
{"messages": [{"content": "Let UJ = 8. Let H be the reflection of point J across point U. Let V be the rotation of point U by angle 11pi/12 around point J. Point P is obtained by rotating point U by angle 2pi/3 about point H. Line M passes through point J perpendicular to segment UH. Point E is the reflection of point P across line M. Point X is the reflection of point V across segment UH. Line G passes through point X parallel to segment UH. Let Y be the angle bisector of angle EHP. Point Z is the reflection of point P across line Y. Point S is the reflection of point Z across line G. Point D is the reflection of point Z across point S. What is the length of segment UD? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.75", "dataset": "MATH"}
{"messages": [{"content": "Let PD = 4. Point L is the reflection of point P across point D. Let Z be the midpoint of segment LD. Let M be the rotation of point P by angle 3pi/4 around point Z. Point T is the reflection of point L across point M. Line X is the perpendicular bisector of segment MD. Point B is the midpoint of segment TP. Let U be the reflection of line X through point L. Point W is the intersection of segment MZ and line U. Point R is the reflection of point W across segment BL. Find the measure of angle ZWR, in radians. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.75", "dataset": "MATH"}
{"messages": [{"content": "Let IO = 2. Let A be the reflection of point O across point I. Line J passes through points A and O. Let F be the line through point A perpendicular to line J. Point H is on line F with |HI| = 1. Let Q be the angle bisector of angle HIO. Point S is the reflection of point O across point A. Let D be the reflection of line Q through point O. Point G is the reflection of point S across line D. Find the length of segment GS. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.46", "dataset": "MATH"}
{"messages": [{"content": "FW = 12. Line S is the perpendicular bisector of segment FW. Point Y is the reflection of point W across point F. Let A be the rotation of point W by angle pi/2 around point Y. Let Q be the midpoint of segment YA. Point O is the midpoint of segment AF. Line I passes through points A and F. Line G is the reflection of line S across point O. Let K be the reflection of line G across line I. Let B be the midpoint of segment OA. Let C be the reflection of point B across point Q. Point P is the reflection of point F across line K. Point M is the reflection of point B across line K. Point L is the reflection of point A across point C. Line H passes through point M perpendicular to line G. Point U is the reflection of point P across line H. Find the length of segment LU. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62.23", "dataset": "MATH"}
{"messages": [{"content": "Let KX = 11. Line Z passes through points X and K. Point F is obtained by rotating point X by angle 7pi/12 about point K. Let M be the line through points K and F. Line C is the reflection of line M across line Z. Let I be the reflection of point K across point X. Let L be the line through point F perpendicular to segment XF. Point V is the midpoint of segment XF. Point T is the reflection of point I across line C. Point D is the reflection of point V across line L. Find the distance between points T and D. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.51", "dataset": "MATH"}
{"messages": [{"content": "Let ND = 9. Point Z is obtained by rotating point D by angle pi/3 about point N. Line A is the perpendicular bisector of segment NZ. Point S is the midpoint of segment DZ. Let J be the rotation of point N by angle 7pi/12 around point D. Point Q is the reflection of point S across line A. Let K be the perpendicular bisector of segment QJ. Let L be the midpoint of segment SQ. Point U lies on line K. Let W be the rotation of point L by angle 2pi/3 around point S. Point F is the reflection of point W across segment NZ. Point X is the reflection of point D across segment NZ. Point G is the midpoint of segment XU. Let V be the midpoint of segment FG. Point I is the midpoint of segment GN. What is the distance between points V and I? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.9", "dataset": "MATH"}
{"messages": [{"content": "Let WN = 1. Point V is obtained by rotating point W by angle pi/2 about point N. Let Y be the line through points N and V. Point R is the reflection of point W across line Y. Let X be the reflection of point V across point N. Q is placed 4 units away from R. Point F is the reflection of point Q across point N. Point T is on line Y with |TQ| = 2. Let S be the angle bisector of angle QTF. Point L is on line S with |LQ| = 7. Let I be the line through point T perpendicular to line S. Point K is the reflection of point L across line I. Line A is the perpendicular bisector of segment XK. Point E is the reflection of point R across line A. What is the length of segment EK? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.41", "dataset": "MATH"}
{"messages": [{"content": "FL = 1. Let G be the reflection of point F across point L. Let S be the reflection of point F across point G. Line P is the angle bisector of angle FLG. Point H is the reflection of point S across line P. Line T is the perpendicular bisector of segment GS. Let B be the rotation of point F by angle pi/12 around point H. Point U is the midpoint of segment HB. Point I is the reflection of point B across line T. Line Q passes through points G and U. Point V is the intersection of segment IL and line Q. What is the length of segment SV? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.55", "dataset": "MATH"}
{"messages": [{"content": "MB = 10. Point A is the reflection of point B across point M. Let G be the reflection of point B across point A. Point N is the midpoint of segment MB. Let W be the angle bisector of angle GNB. Line R is the reflection of line W across point G. Point U is the reflection of point M across line R. What is the distance between points U and N? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "135.0", "dataset": "MATH"}
{"messages": [{"content": "Let ZK = 2. Let B be the midpoint of segment ZK. Point V is obtained by rotating point B by angle 11pi/12 about point K. Let J be the line through points K and Z. Let T be the perpendicular bisector of segment VB. Let D be the midpoint of segment BK. Line I is the reflection of line T across line J. Point C is the reflection of point Z across point D. Let M be the reflection of point V across point C. Line O passes through points M and C. Line H is the reflection of line O across line J. Let W be the reflection of line O across line I. Lines W and H intersect at point F. Line H and segment MZ intersect at point N. What is the distance between points N and F? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.66", "dataset": "MATH"}
{"messages": [{"content": "Let JS = 8. Point X is the midpoint of segment JS. Line O is the perpendicular bisector of segment SJ. Let V be the midpoint of segment JX. Point G is the midpoint of segment SV. Point Y lies on line O at distance 3 from point G. Point B is the midpoint of segment YJ. Let N be the midpoint of segment BS. Let Q be the reflection of point N across point S. Line K is the perpendicular bisector of segment QG. Point R is the reflection of point B across line K. Let P be the reflection of point B across point Y. Find the length of segment PR. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.44", "dataset": "MATH"}
{"messages": [{"content": "JR = 7. Line V passes through point R perpendicular to segment JR. Point P is the reflection of point R across point J. Let A be the reflection of line V through point J. Let I be the reflection of line A across line V. Point H is the reflection of point J across line I. Point Z is the midpoint of segment HR. Find the distance between points P and Z. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31.5", "dataset": "MATH"}
{"messages": [{"content": "Let QA = 11. Let V be the vector from point A to point Q. Point D is the translation of point Q by vector V. Line U passes through points A and D. Let W be the reflection of point A across point D. Point K is obtained by rotating point W by angle pi/4 about point A. Line Z is the angle bisector of angle KQA. Point H is the reflection of point K across point D. Point B is the translation of point K by vector V. Let T be the line through point H perpendicular to line Z. Point F is the midpoint of segment HD. Let Y be the reflection of line U through point F. Point M is obtained by rotating point Q by angle 2pi/3 about point K. Point G is the midpoint of segment WB. Line O passes through point M perpendicular to line T. Line P is the reflection of line O across line Y. Point C is the reflection of point K across line P. Find the distance between points C and G. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "164.48", "dataset": "MATH"}
{"messages": [{"content": "FN = 7. Point G is the midpoint of segment FN. Point S is obtained by rotating point F by angle 7pi/12 about point G. Let Z be the rotation of point F by angle pi/4 around point S. Let E be the midpoint of segment ZS. Point W is the reflection of point F across point E. Point R is the midpoint of segment EG. What is the distance between points W and R? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.66", "dataset": "MATH"}
{"messages": [{"content": "Let AC = 8. Let D be the rotation of point A by angle 7pi/12 around point C. Let F be the angle bisector of angle ADC. Let Z be the midpoint of segment DA. Let Q be the reflection of point C across point A. Let X be the line through point D parallel to segment AC. Line L is the reflection of line X across line F. Line E passes through point Z parallel to line L. Let V be the rotation of point Q by angle 11pi/12 around point A. Line O passes through point A perpendicular to segment AC. Point W is the reflection of point V across point C. Line N is the reflection of line O across line E. Lines X and N intersect at point H. Point I is the reflection of point W across segment AC. What is the distance between points I and H? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.66", "dataset": "MATH"}
{"messages": [{"content": "Let PD = 8. Let Q be the perpendicular bisector of segment DP. Point I lies on line Q at distance 9 from point D. Point J is the reflection of point P across segment DI. Let Z be the midpoint of segment PI. Find the length of segment ZJ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.45", "dataset": "MATH"}
{"messages": [{"content": "Let WY = 8. Let I be the rotation of point Y by angle 2pi/3 around point W. Line S is the perpendicular bisector of segment WI. Let P be the line through point W parallel to line S. Line P and segment IY intersect at point A. Point X is the reflection of point A across segment YW. Find the distance between points A and X. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.62", "dataset": "MATH"}
{"messages": [{"content": "Let IO = 5. Let Y be the rotation of point I by angle pi/12 around point O. S is placed 6 units away from O. Let Q be the angle bisector of angle SOI. Point Z is the reflection of point S across line Q. Let A be the rotation of point I by angle pi/3 around point Z. Point U is the reflection of point Y across segment ZI. Let M be the rotation of point O by angle 11pi/12 around point U. Let N be the midpoint of segment YM. Point K is the intersection of segments NO and UA. Find the length of segment IK. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.02", "dataset": "MATH"}
{"messages": [{"content": "Let LX = 10. Let Y be the reflection of point L across point X. Let A be the rotation of point L by angle 3pi/4 around point Y. Point R is the reflection of point A across point X. Line B is the angle bisector of angle RAL. Let G be the line through point L perpendicular to segment XA. Line I is the reflection of line B across point L. Line Z is the reflection of line I across line G. Lines Z and I intersect at point M. Find the length of segment RM. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.79", "dataset": "MATH"}
{"messages": [{"content": "PA = 7. Point Y is the midpoint of segment AP. Point N is the reflection of point A across point P. Let I be the angle bisector of angle NPA. Let E be the midpoint of segment NP. Line M is the perpendicular bisector of segment AP. Let L be the rotation of point A by angle pi/4 around point N. Line V is the reflection of line I across line M. Line O is the reflection of line V across point N. Point U is the reflection of point L across point E. Let B be the reflection of point U across point Y. Point J is the reflection of point Y across line O. What is the distance between points J and B? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63.18", "dataset": "MATH"}
{"messages": [{"content": "TG = 2. Let Y be the vector from point G to point T. Point E is the midpoint of segment GT. Point D is the translation of point T by vector Y. Let S be the perpendicular bisector of segment ED. Point J is obtained by rotating point T by angle 5pi/6 about point G. Line X passes through point G parallel to line S. Point B is the midpoint of segment EJ. Point W is the reflection of point T across line S. Point F is the intersection of line X and segment BD. Find the distance between points W and F. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.03", "dataset": "MATH"}
{"messages": [{"content": "Let TG = 6. Point N is obtained by rotating point G by angle 3pi/4 about point T. Let C be the rotation of point T by angle pi/6 around point N. Line W passes through points N and C. Point D is the reflection of point T across line W. Let H be the line through point G parallel to line W. Point L is the reflection of point D across line H. Find the length of segment LD. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.89", "dataset": "MATH"}
{"messages": [{"content": "PC = 8. Let A be the perpendicular bisector of segment PC. Point Y is obtained by rotating point P by angle pi/12 about point C. Let O be the line through point P parallel to line A. Line N passes through point Y parallel to line O. Point L is the reflection of point P across segment YC. Let W be the rotation of point L by angle 3pi/4 around point Y. Point H is the reflection of point C across point Y. Let G be the line through point W perpendicular to segment YC. Line R is the reflection of line O across line G. Lines N and R intersect at point D. Find the length of segment HD. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.79", "dataset": "MATH"}
{"messages": [{"content": "LY = 10. Let M be the perpendicular bisector of segment YL. Line J is the reflection of line M across point L. Line K is the reflection of line J across point Y. Point H is the reflection of point Y across line J. Point T is the midpoint of segment HL. Let I be the rotation of point H by angle 11pi/12 around point Y. Let S be the rotation of point T by angle 3pi/4 around point I. Point G is the intersection of segment LI and line K. Point A is the reflection of point G across line J. Let V be the midpoint of segment SI. Find the length of segment VA. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91.45", "dataset": "MATH"}
{"messages": [{"content": "YA = 6. Let J be the midpoint of segment AY. Point S is obtained by rotating point Y by angle pi/6 about point J. Line X is the angle bisector of angle SYA. Point E is the reflection of point J across point A. Let T be the line through point S parallel to line X. Point R is the reflection of point E across point S. Point B is the reflection of point Y across line T. Find the distance between points B and R. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.2", "dataset": "MATH"}
{"messages": [{"content": "DN = 6. Point T is obtained by rotating point D by angle pi/3 about point N. Point C is the midpoint of segment DT. Line L passes through point N parallel to segment DT. Let M be the midpoint of segment CD. Let V be the midpoint of segment MT. Let U be the perpendicular bisector of segment DT. Point K is the reflection of point V across line U. Point I is the reflection of point V across line L. What is the length of segment KI? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.5", "dataset": "MATH"}
{"messages": [{"content": "Let XU = 4. Point R is the reflection of point X across point U. C is placed 7 units away from R. Point O is the reflection of point C across segment XU. Line G is the perpendicular bisector of segment OR. Let P be the midpoint of segment XU. Point J is the reflection of point P across line G. Find the distance between points J and O. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.0", "dataset": "MATH"}
{"messages": [{"content": "Let FC = 11. Let Z be the midpoint of segment CF. Point M is obtained by rotating point C by angle 7pi/12 about point Z. Point D is obtained by rotating point Z by angle pi/6 about point M. Let L be the line through point M perpendicular to segment CM. Let Y be the vector from point M to point F. Let O be the reflection of point M across point Z. Point V is the translation of point O by vector Y. Point E is the translation of point V by vector Y. Line T is the perpendicular bisector of segment VE. Point G is the reflection of point C across line T. Point B is the midpoint of segment CM. Point H is the reflection of point E across line L. Let I be the reflection of point H across point D. Line S is the angle bisector of angle BCG. Point P is the reflection of point D across line S. Find the length of segment IP. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.82", "dataset": "MATH"}
{"messages": [{"content": "GD = 9. Point Q is obtained by rotating point G by angle 5pi/6 about point D. Let V be the perpendicular bisector of segment GD. Point H is obtained by rotating point G by angle 7pi/12 about point D. Line T passes through point G parallel to line V. Let U be the reflection of point D across point Q. Point J is the reflection of point H across line T. Let N be the reflection of line T across line V. Line F passes through point U perpendicular to line N. Point R is on line F. Let C be the reflection of point R across point J. Point E is the reflection of point C across line N. What is the length of segment RE? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40.66", "dataset": "MATH"}
{"messages": [{"content": "VY = 1. Let M be the midpoint of segment YV. Let B be the perpendicular bisector of segment YV. Let F be the rotation of point Y by angle 7pi/12 around point V. Point S is the reflection of point M across point V. Let T be the midpoint of segment SV. Let P be the midpoint of segment FM. Point C is the reflection of point S across line B. Point N is the reflection of point C across segment FM. Let R be the midpoint of segment FP. Let J be the reflection of point R across point S. Let D be the line through point J perpendicular to segment CN. Point I is the reflection of point Y across line D. Find the length of segment IT. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.05", "dataset": "MATH"}
{"messages": [{"content": "TP = 2. Point X is the reflection of point P across point T. Let W be the rotation of point T by angle pi/3 around point P. Point K is the reflection of point W across point T. Let L be the midpoint of segment XK. Line O passes through points T and P. Point V lies on segment KL. Point N is the reflection of point V across line O. What is the measure of angle NVK, in radians? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.62", "dataset": "MATH"}
{"messages": [{"content": "TG = 8. Let W be the midpoint of segment GT. X is constructed so that GX = 5. B is placed 5 units away from W. Point N is obtained by rotating point T by angle 5pi/12 about point X. Line Q is the angle bisector of angle WXN. Let J be the midpoint of segment WB. Let K be the line through point J perpendicular to line Q. Point M is the reflection of point W across line K. What is the distance between points J and M? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Let IM = 2. Point A is the reflection of point M across point I. Line F passes through points A and I. Point O lies on line F. Line C is the perpendicular bisector of segment MI. Let P be the reflection of point M across point O. Let X be the perpendicular bisector of segment OM. Point G is the reflection of point O across line C. Point Z is the reflection of point G across line X. Find the distance between points P and Z. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "RW = 9. Let Y be the rotation of point W by angle 11pi/12 around point R. Line Q is the perpendicular bisector of segment YR. Let U be the rotation of point W by angle pi/2 around point R. Let X be the line through point W perpendicular to line Q. Point A is obtained by rotating point Y by angle 3pi/4 about point U. Point V is obtained by rotating point Y by angle 5pi/12 about point W. Point Z is the reflection of point R across line X. Point J is the reflection of point Y across segment VZ. Let L be the angle bisector of angle AWV. Point N is the reflection of point W across segment VZ. Let D be the line through point J perpendicular to segment VZ. Point T is the reflection of point N across line D. Point C is the reflection of point T across line L. What is the length of segment CJ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.05", "dataset": "MATH"}
{"messages": [{"content": "Let HE = 11. Point U is the midpoint of segment HE. Point J is obtained by rotating point U by angle 2pi/3 about point E. Let W be the angle bisector of angle HJU. Let O be the line through point E parallel to line W. Let D be the reflection of point J across point H. Point L is on line O with |LU| = 5. Point R is the reflection of point U across line O. Let Y be the line through point D parallel to line O. Line X is the reflection of line Y across point L. Point M is the reflection of point D across line X. Let T be the midpoint of segment MR. What is the length of segment MT? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.47", "dataset": "MATH"}
{"messages": [{"content": "NU = 10. Point Z is obtained by rotating point N by angle 3pi/4 about point U. Let R be the reflection of point N across point U. Point L is obtained by rotating point Z by angle pi/2 about point R. Line H passes through point L parallel to segment NR. Let P be the midpoint of segment ZL. Point X is the reflection of point L across segment NR. Point C is the reflection of point P across line H. What is the measure of angle CLX, in radians? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.18", "dataset": "MATH"}
{"messages": [{"content": "Let NM = 10. Point W is the reflection of point N across point M. Let Z be the rotation of point M by angle 2pi/3 around point W. Let K be the reflection of point Z across point N. Line X passes through points Z and N. Point A is the reflection of point K across point Z. Let P be the line through point A perpendicular to line X. Point L is the reflection of point Z across line P. Let O be the reflection of point L across point M. What is the distance between points O and A? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "192.87", "dataset": "MATH"}
{"messages": [{"content": "BY = 11. Point M is obtained by rotating point B by angle pi/4 about point Y. Point C is the midpoint of segment MB. Point E is obtained by rotating point Y by angle 11pi/12 about point C. Let J be the reflection of point Y across point B. Line U passes through point J perpendicular to segment YB. Point R is the reflection of point E across line U. Let Q be the reflection of point R across point E. What is the length of segment QC? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.18", "dataset": "MATH"}
{"messages": [{"content": "Let PF = 12. Point W is obtained by rotating point F by angle 5pi/6 about point P. Let A be the rotation of point P by angle pi/6 around point F. Let V be the midpoint of segment FP. Point B is the midpoint of segment AW. Line K is the angle bisector of angle PAB. Let O be the perpendicular bisector of segment VF. Let R be the reflection of line K through point V. Let U be the line through point F parallel to line O. Point M is the intersection of lines R and U. Find the distance between points M and V. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.81", "dataset": "MATH"}
{"messages": [{"content": "Let LK = 12. Line G passes through points K and L. Let Z be the reflection of point K across point L. Let X be the rotation of point K by angle 2pi/3 around point L. Line P passes through point L perpendicular to line G. Point V is the midpoint of segment XL. Line A is the reflection of line P across point K. Point C is obtained by rotating point V by angle 5pi/12 about point L. Line N is the perpendicular bisector of segment KC. Line R passes through point Z parallel to line N. Line T is the reflection of line R across line A. Lines G and T intersect at point J. What is the distance between points J and C? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65.81", "dataset": "MATH"}
{"messages": [{"content": "HU = 7. Line F is the perpendicular bisector of segment HU. Point T lies on line F at distance 9 from point U. Let K be the reflection of point T across point U. Let S be the rotation of point K by angle 5pi/12 around point T. Let P be the midpoint of segment UT. Let O be the midpoint of segment SU. Point D is the reflection of point P across point O. Let G be the reflection of point T across point D. Point W is the reflection of point O across point U. What is the distance between points W and G? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47.26", "dataset": "MATH"}
{"messages": [{"content": "Let SQ = 9. Let C be the reflection of point Q across point S. Let N be the rotation of point C by angle 3pi/4 around point S. Let V be the midpoint of segment QS. Line K is the perpendicular bisector of segment CQ. Point R is the reflection of point N across line K. Point B is the reflection of point N across point Q. Let L be the reflection of point V across point C. Point Y is the reflection of point B across segment NV. Let T be the line through points Y and S. Line G passes through point R perpendicular to line T. Point J is the reflection of point L across line G. Point P is the midpoint of segment NV. Find the distance between points P and J. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.62", "dataset": "MATH"}
{"messages": [{"content": "ZA = 3. Let H be the reflection of point A across point Z. Point O is obtained by rotating point A by angle 2pi/3 about point H. Point T is the reflection of point Z across point H. Point X is the midpoint of segment HZ. Let P be the line through point X perpendicular to segment XO. Line L is the reflection of line P across point T. Line L and segment XO intersect at point F. Find the distance between points O and F. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.98", "dataset": "MATH"}
{"messages": [{"content": "UD = 3. Let C be the reflection of point D across point U. Line F is the perpendicular bisector of segment UC. Point H is the reflection of point D across line F. Line N is the angle bisector of angle DCH. Let Q be the reflection of line N through point U. Point W is the reflection of point C across line Q. What is the distance between points W and C? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.0", "dataset": "MATH"}
{"messages": [{"content": "TX = 2. Point L is the midpoint of segment TX. Point E is the midpoint of segment XL. Let A be the midpoint of segment EX. What is the distance between points L and A? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
{"messages": [{"content": "Let LE = 3. Let Q be the line through point L perpendicular to segment EL. Point B is on line Q. Point T is the midpoint of segment EL. Point R is the reflection of point B across segment EL. Let A be the midpoint of segment TR. Point C is the reflection of point A across line Q. What is the length of segment CA? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "QP = 7. Point C is the midpoint of segment PQ. Let K be the rotation of point P by angle 11pi/12 around point C. Point X is the midpoint of segment QK. Let D be the reflection of point K across point P. Point N is the midpoint of segment PD. Let Y be the midpoint of segment XN. Let Z be the reflection of point C across point D. Point R is the reflection of point Y across segment QZ. Find the distance between points C and R. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.86", "dataset": "MATH"}
{"messages": [{"content": "Let CG = 9. Let Q be the rotation of point C by angle pi/12 around point G. Point L is obtained by rotating point C by angle 2pi/3 about point G. Let D be the rotation of point L by angle 5pi/6 around point Q. Point H is the reflection of point D across segment QC. Point S is the reflection of point H across segment QL. Point Z is the midpoint of segment QG. Let U be the reflection of point D across point Z. Find the distance between points S and U. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.23", "dataset": "MATH"}
{"messages": [{"content": "Let DX = 8. Let B be the midpoint of segment XD. Let Q be the perpendicular bisector of segment BD. Point V is obtained by rotating point B by angle pi/6 about point X. Let P be the rotation of point X by angle 11pi/12 around point D. Line W is the perpendicular bisector of segment PB. Let N be the reflection of line Q across line W. Let A be the midpoint of segment PB. Let S be the line through point B parallel to line Q. Point F is the reflection of point V across line Q. Point U is the reflection of point A across line S. Segment PB and line N intersect at point Z. Point O is the midpoint of segment FZ. Find the distance between points O and U. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.05", "dataset": "MATH"}
{"messages": [{"content": "Let PB = 3. Line H is the perpendicular bisector of segment BP. Point O is obtained by rotating point B by angle 3pi/4 about point P. Line Z is the angle bisector of angle POB. Let Y be the rotation of point P by angle 7pi/12 around point O. Line F is the reflection of line Z across line H. Point V is on line F with |VP| = 7. Line K passes through point B parallel to line F. Let U be the line through points P and V. Point N is the intersection of lines U and K. Line G passes through point Y parallel to line K. Point W is the reflection of point V across line G. Find the distance between points N and W. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.91", "dataset": "MATH"}
{"messages": [{"content": "SX = 3. Let B be the midpoint of segment SX. Let C be the angle bisector of angle SBX. Line F passes through point X parallel to line C. Point Z lies on line F at distance 11 from point B. Point U is the midpoint of segment BX. Line H is the perpendicular bisector of segment UX. Let I be the reflection of line H across line F. Point P is the midpoint of segment ZS. Point G is the reflection of point Z across line I. Let M be the midpoint of segment PU. Find the distance between points G and M. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.46", "dataset": "MATH"}
{"messages": [{"content": "QV = 4. Let H be the midpoint of segment VQ. Let Y be the rotation of point Q by angle 11pi/12 around point H. Line C is the angle bisector of angle QYV. Let A be the line through point V parallel to line C. Point G is the reflection of point H across line A. Point W is the midpoint of segment YQ. Find the length of segment GW. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.36", "dataset": "MATH"}
{"messages": [{"content": "Let AN = 10. Let E be the rotation of point N by angle pi/2 around point A. Let B be the line through point A perpendicular to segment AN. Let S be the reflection of point A across point E. Line K is the perpendicular bisector of segment AN. Line D is the reflection of line B across line K. Point X is the reflection of point E across line D. Point M is the reflection of point X across line K. Point H is the reflection of point M across point S. What is the length of segment AH? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31.62", "dataset": "MATH"}
{"messages": [{"content": "VY = 2. Point D is obtained by rotating point Y by angle 11pi/12 about point V. Line G is the perpendicular bisector of segment YV. Line A passes through point V parallel to line G. Point X is obtained by rotating point V by angle 5pi/6 about point D. Let S be the reflection of line A across line G. Let Z be the perpendicular bisector of segment YD. Line P is the reflection of line G across line Z. Point U is the reflection of point V across point X. Point N is the reflection of point U across line P. Let T be the line through point N parallel to segment YX. Line A and segment YX intersect at point C. Lines T and S intersect at point K. Let M be the reflection of point K across point C. Point O is the reflection of point K across point U. Let Q be the midpoint of segment OM. Find the length of segment KQ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.72", "dataset": "MATH"}
{"messages": [{"content": "Let FC = 12. Point A is obtained by rotating point C by angle 5pi/6 about point F. Let X be the angle bisector of angle ACF. Point K is the reflection of point F across line X. Point I is the reflection of point F across point A. Point O is the midpoint of segment KC. Point U is obtained by rotating point F by angle pi/2 about point I. Let B be the line through points I and U. Point L is the midpoint of segment OC. Let Z be the midpoint of segment UA. Line N is the perpendicular bisector of segment ZI. Point D is the reflection of point K across line N. Point R is the reflection of point L across line B. Let Y be the midpoint of segment DL. Find the length of segment RY. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56.31", "dataset": "MATH"}
{"messages": [{"content": "Let MT = 11. Point L is obtained by rotating point T by angle 5pi/12 about point M. Let U be the vector from point M to point L. Let P be the rotation of point L by angle pi/2 around point T. Point N is the reflection of point T across point M. Line X is the angle bisector of angle TNP. Point G is the translation of point P by vector U. Line R is the perpendicular bisector of segment LG. Point Y is obtained by rotating point T by angle 5pi/6 about point L. Point J is the reflection of point P across line R. Point H is the midpoint of segment NG. Let Q be the line through point L perpendicular to line X. Point B is the reflection of point G across line Q. Point O is the reflection of point M across point P. Point V is the midpoint of segment HB. Point W is the midpoint of segment YJ. Let Z be the line through points V and W. Point A is the reflection of point O across line Z. Point E is the midpoint of segment WA. What is the length of segment OE? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.58", "dataset": "MATH"}
{"messages": [{"content": "VS = 7. Let M be the line through points S and V. Point F is on line M. Let U be the midpoint of segment VS. Let Y be the rotation of point U by angle pi/4 around point V. Line O is the angle bisector of angle FUS. Point J is the reflection of point Y across line O. Point L is the reflection of point S across point J. Let B be the midpoint of segment LJ. Point R is the reflection of point B across point J. Let X be the reflection of point R across point B. What is the distance between points V and X? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.24", "dataset": "MATH"}
{"messages": [{"content": "IN = 2. Let D be the perpendicular bisector of segment NI. Line L is the reflection of line D across point I. Point Z is the reflection of point N across point I. Let K be the midpoint of segment IN. Point Q is the reflection of point N across line L. Let J be the rotation of point K by angle 5pi/6 around point N. Let W be the rotation of point Q by angle 3pi/4 around point K. Line M is the perpendicular bisector of segment QJ. Point Y is the intersection of line L and segment WZ. Line T passes through points N and Y. Let C be the reflection of line T across line M. Point A is the reflection of point J across line C. Point O is the midpoint of segment AI. Find the distance between points O and Z. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.34", "dataset": "MATH"}
{"messages": [{"content": "GN = 8. Point Y is the reflection of point N across point G. Let A be the perpendicular bisector of segment NG. Let R be the reflection of line A through point Y. Point S is the reflection of point Y across line R. Let Q be the midpoint of segment SG. Let J be the perpendicular bisector of segment SN. Let P be the rotation of point N by angle 2pi/3 around point G. Point X is the reflection of point G across line J. Point O is the reflection of point P across line J. Point F is the reflection of point P across segment NG. Point D is the reflection of point G across point O. Point I is the reflection of point Q across segment XP. Let K be the midpoint of segment ID. What is the length of segment FK? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29.74", "dataset": "MATH"}
{"messages": [{"content": "Let WP = 3. Point C is obtained by rotating point P by angle pi/12 about point W. Point R is the midpoint of segment CP. Let M be the midpoint of segment WP. Point K is the reflection of point R across segment CW. What is the length of segment MK? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.69", "dataset": "MATH"}
{"messages": [{"content": "EQ = 2. Point F is obtained by rotating point Q by angle pi/6 about point E. Let K be the rotation of point E by angle pi around point F. Point U is the reflection of point K across point E. Line C is the angle bisector of angle UQK. Let M be the reflection of point K across point U. Point X is the reflection of point M across line C. Find the distance between points X and U. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.1", "dataset": "MATH"}
{"messages": [{"content": "GQ = 11. Point M is the reflection of point Q across point G. Point Y is obtained by rotating point M by angle pi/12 about point Q. Point U is the reflection of point Y across point G. Point A is obtained by rotating point M by angle pi/3 about point U. Point Z is the reflection of point G across point A. Point X is the midpoint of segment ZU. Point H is the reflection of point A across segment ZU. What is the length of segment HX? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.86", "dataset": "MATH"}
{"messages": [{"content": "EC = 6. Point V is the midpoint of segment EC. Point J is the reflection of point V across point E. Let D be the midpoint of segment JC. Let H be the perpendicular bisector of segment JD. Point B is the reflection of point E across line H. What is the distance between points B and E? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "GC = 7. Let Y be the midpoint of segment CG. Line F is the angle bisector of angle CGY. Let K be the line through point Y perpendicular to line F. Line X passes through point G parallel to line K. Let M be the reflection of point G across point C. Point D is on line X with |DM| = 3. Point A is the reflection of point D across line F. Point R is the midpoint of segment MA. Let V be the angle bisector of angle GAR. Point J is the reflection of point M across line V. Let Z be the midpoint of segment JC. Find the distance between points Z and J. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.65", "dataset": "MATH"}
{"messages": [{"content": "BR = 5. Line Y passes through points B and R. Point A is the midpoint of segment RB. Let F be the rotation of point R by angle 5pi/12 around point A. Point L is the reflection of point F across line Y. Line M passes through point L parallel to line Y. Let G be the line through point F parallel to line Y. Point W is on line M. Point K is the reflection of point W across line G. What is the length of segment WK? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.66", "dataset": "MATH"}
{"messages": [{"content": "TG = 8. Point I is the reflection of point G across point T. Let Z be the rotation of point I by angle 7pi/12 around point G. Let R be the line through points I and Z. Point N is the midpoint of segment ZG. Let K be the midpoint of segment IN. Point O is the reflection of point K across line R. Let A be the reflection of point N across point G. Let S be the midpoint of segment KA. Let H be the midpoint of segment OG. Point P is the reflection of point H across point N. Point U is the reflection of point S across point N. Find the distance between points U and P. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.81", "dataset": "MATH"}
{"messages": [{"content": "Let GM = 12. Let U be the perpendicular bisector of segment GM. Line K passes through point M parallel to line U. Point J lies on line K at distance 8 from point G. Point A lies on line K at distance 6 from point G. Let V be the perpendicular bisector of segment AM. Let H be the midpoint of segment AJ. Point Z is the reflection of point H across line V. Point L is the midpoint of segment AG. Find the length of segment ZL. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.21", "dataset": "MATH"}
{"messages": [{"content": "DX = 9. Let B be the vector from point X to point D. Let I be the midpoint of segment DX. Point F is obtained by rotating point X by angle 7pi/12 about point D. Let L be the midpoint of segment FD. Point Y is the midpoint of segment LX. Point Z is the translation of point I by vector B. Let J be the midpoint of segment ZL. Let P be the midpoint of segment JY. Point W is the reflection of point Z across point P. Point A is the reflection of point P across segment FL. Point G is the midpoint of segment WA. Point H is the midpoint of segment GI. What is the length of segment HJ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.13", "dataset": "MATH"}
{"messages": [{"content": "KX = 10. Point B is the reflection of point X across point K. Let R be the reflection of point X across point B. Let D be the vector from point B to point K. Let E be point R translated by vector D. Point U is obtained by rotating point K by angle pi/6 about point X. Let M be the midpoint of segment EU. Point O is the reflection of point B across point U. Point N is the reflection of point K across point M. Point W is the reflection of point N across segment KE. What is the distance between points W and O? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34.74", "dataset": "MATH"}
{"messages": [{"content": "Let TC = 2. Point P is the reflection of point T across point C. Let V be the vector from point T to point C. Let B be the rotation of point P by angle pi/6 around point T. Let W be the angle bisector of angle CBP. Point G is the reflection of point C across point P. Point U is the reflection of point B across point C. Point M is obtained by rotating point B by angle 11pi/12 about point U. Let E be the line through point T parallel to line W. Point H is the translation of point M by vector V. Let Z be the line through points T and P. Point F is obtained by rotating point H by angle 5pi/12 about point C. Point O is the midpoint of segment MP. Point D is the reflection of point G across point F. Let N be the reflection of line Z across line E. Point K is the reflection of point O across line N. Find the length of segment DK. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.51", "dataset": "MATH"}
{"messages": [{"content": "Let OM = 5. Let B be the reflection of point O across point M. Point Q is obtained by rotating point O by angle 7pi/12 about point M. Line H is the perpendicular bisector of segment OQ. Point C is the midpoint of segment BM. Let Z be the perpendicular bisector of segment BQ. Let W be the line through point O perpendicular to line Z. Point X is the reflection of point C across point Q. Point D is the reflection of point X across line W. Let S be the reflection of point C across point D. Point A is the reflection of point C across line H. Find the distance between points A and S. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33.23", "dataset": "MATH"}
{"messages": [{"content": "KD = 7. Let G be the midpoint of segment KD. Let I be the rotation of point G by angle pi/2 around point K. Point Y is the reflection of point I across point G. Let E be the line through points I and D. Let U be the line through point D perpendicular to line E. Let L be the reflection of line U through point I. Point Z is the reflection of point Y across line L. Find the distance between points I and Z. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25.24", "dataset": "MATH"}
{"messages": [{"content": "Let IP = 3. Point R is the reflection of point I across point P. Point O is obtained by rotating point R by angle pi/3 about point I. Point H is obtained by rotating point P by angle pi/4 about point I. Line Q is the angle bisector of angle HIP. Line Y passes through point R parallel to line Q. Point N is obtained by rotating point H by angle pi about point P. Point Z is the midpoint of segment ON. Let V be the perpendicular bisector of segment IH. Let W be the line through point N perpendicular to line Y. Point T is the reflection of point I across point Z. Line X is the reflection of line V across point R. Point S is the midpoint of segment PT. Point L is the reflection of point N across line X. Point K is the reflection of point S across line W. What is the length of segment KL? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.07", "dataset": "MATH"}
{"messages": [{"content": "Let QC = 7. Line F passes through point Q perpendicular to segment QC. Point N lies on line F at distance 6 from point Q. Point K is the reflection of point C across point N. Let X be the midpoint of segment QC. Let Z be the midpoint of segment XQ. Point V is the reflection of point K across segment QC. Point E is the reflection of point Z across segment QK. What is the length of segment EV? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.14", "dataset": "MATH"}
{"messages": [{"content": "SM = 12. Let V be the midpoint of segment SM. Point A is obtained by rotating point V by angle 11pi/12 about point M. SX = 4. Let K be the reflection of point V across point A. Let Z be the reflection of point V across point X. Let R be the angle bisector of angle XZA. Point W lies on line R at distance 2 from point S. Point J is the midpoint of segment MK. Let E be the line through point W parallel to segment MK. Line H passes through point A perpendicular to line E. Line I passes through point J parallel to line H. Point Y is the reflection of point S across line I. What is the length of segment YK? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.0", "dataset": "MATH"}
{"messages": [{"content": "PS = 2. Let Z be the reflection of point S across point P. Point N is obtained by rotating point P by angle 7pi/12 about point Z. Point I is the midpoint of segment SP. Let D be the rotation of point I by angle pi/2 around point N. Line E is the angle bisector of angle SNP. Point V is the midpoint of segment SD. Line U is the perpendicular bisector of segment DI. Point F is the reflection of point P across point N. Line H passes through point I parallel to line E. Let G be the rotation of point S by angle 2pi/3 around point I. Let T be the line through points G and V. Let Q be the reflection of line U across line T. Let K be the line through point Z parallel to line Q. Point R is the intersection of lines H and K. Point O is the reflection of point F across point D. What is the distance between points O and R? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61.57", "dataset": "MATH"}
{"messages": [{"content": "Let CL = 10. Point Q is the midpoint of segment LC. Let M be the rotation of point Q by angle pi/3 around point L. Point E is obtained by rotating point L by angle pi/4 about point Q. Let H be the vector from point E to point L. Let V be the perpendicular bisector of segment QE. Point W is the reflection of point M across line V. Point T is the translation of point W by vector H. Point Z is the midpoint of segment CT. Point F is the midpoint of segment TZ. Let Y be the midpoint of segment FQ. Point D is the reflection of point Y across segment LW. Find the distance between points D and C. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.79", "dataset": "MATH"}
{"messages": [{"content": "KM = 1. Let E be the rotation of point K by angle 2pi/3 around point M. Let S be the reflection of point E across point K. Let X be the reflection of point M across point K. Line P is the angle bisector of angle MSK. Point A is the reflection of point X across line P. Point B is the reflection of point A across segment EX. Point G is the reflection of point M across segment EX. Point F is the reflection of point G across point B. Find the distance between points F and E. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.62", "dataset": "MATH"}
{"messages": [{"content": "YO = 4. Let X be the rotation of point Y by angle 5pi/6 around point O. Point K is obtained by rotating point X by angle pi/6 about point Y. Let Q be the perpendicular bisector of segment OY. Point D is the reflection of point X across line Q. Let E be the midpoint of segment DO. Point F is the midpoint of segment EK. What is the length of segment DF? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.74", "dataset": "MATH"}
{"messages": [{"content": "Let TY = 8. Let I be the vector from point T to point Y. Let D be point Y translated by vector I. Line M is the perpendicular bisector of segment TD. Point O is the midpoint of segment YT. Point J is the reflection of point D across point O. Point X is the reflection of point J across point Y. Let C be the perpendicular bisector of segment JY. Point W is on line C with |WX| = 8. Line B is the reflection of line C across line M. Let E be the line through point J parallel to line B. Point V is the reflection of point Y across line E. Point S is the midpoint of segment VW. What is the distance between points V and S? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.65", "dataset": "MATH"}
{"messages": [{"content": "Let WE = 5. Line S is the perpendicular bisector of segment WE. Point I is the midpoint of segment WE. Point R is obtained by rotating point W by angle 11pi/12 about point E. Line K passes through points R and W. Point L is the reflection of point I across line K. Line D passes through point L parallel to line S. Let Y be the reflection of line D through point I. Point C is the reflection of point R across line Y. Find the length of segment CI. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.28", "dataset": "MATH"}
{"messages": [{"content": "Let NA = 7. Point K is the midpoint of segment NA. Line U is the perpendicular bisector of segment AK. Let B be the line through point N parallel to line U. Point R is the reflection of point K across line B. Find the distance between points K and R. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.0", "dataset": "MATH"}
{"messages": [{"content": "Let RV = 11. Point D is obtained by rotating point R by angle pi/12 about point V. Let T be the midpoint of segment RV. Line C is the angle bisector of angle DTV. Let Y be the rotation of point D by angle pi/2 around point V. Line B passes through point V perpendicular to line C. Let K be the reflection of point Y across point R. Let L be the reflection of line B through point T. Point Q is the reflection of point D across line L. Let I be the reflection of point K across point Q. What is the distance between points K and I? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30.13", "dataset": "MATH"}
{"messages": [{"content": "Let QF = 9. Let X be the midpoint of segment FQ. Line I passes through points X and Q. Point L is the midpoint of segment XQ. Let G be the reflection of point Q across point F. Point D is obtained by rotating point F by angle pi/2 about point L. Let K be the perpendicular bisector of segment XF. Point A is the reflection of point X across point D. Line P passes through points A and Q. Let U be the reflection of line P across line K. Point H is the midpoint of segment DG. Line C is the reflection of line I across point H. Point S is the intersection of lines C and U. What is the length of segment SH? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.77", "dataset": "MATH"}
{"messages": [{"content": "KO = 9. Point I is obtained by rotating point K by angle 3pi/4 about point O. Let R be the midpoint of segment OK. Line G is the perpendicular bisector of segment KO. Point A is the midpoint of segment OI. Let Q be the line through point A parallel to line G. Point B is obtained by rotating point I by angle pi/2 about point A. Let X be the reflection of line G across line Q. Point P is the reflection of point I across point B. Point F is the reflection of point R across line X. Let Y be the perpendicular bisector of segment IK. Let T be the line through point P parallel to line Y. Point N is the reflection of point R across line T. Let D be the midpoint of segment NF. What is the distance between points D and P? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.79", "dataset": "MATH"}
{"messages": [{"content": "JM = 11. Point F is the midpoint of segment MJ. Let I be the reflection of point F across point M. Point D is the midpoint of segment IM. Point C is the reflection of point D across point I. Find the distance between points D and C. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.5", "dataset": "MATH"}
{"messages": [{"content": "UB = 11. Let E be the rotation of point B by angle 5pi/6 around point U. Let F be the midpoint of segment BU. Point N is the midpoint of segment EF. Let H be the rotation of point B by angle pi around point E. Point I is the reflection of point N across segment FB. Let V be the vector from point F to point U. Let Y be point I translated by vector V. Line C is the perpendicular bisector of segment FB. Let X be the line through point Y parallel to line C. Point G is the reflection of point N across line X. Point D is the reflection of point H across point Y. Point A is the midpoint of segment IG. Find the length of segment DA. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.93", "dataset": "MATH"}
{"messages": [{"content": "LR = 1. Point Y is the reflection of point L across point R. Point I is the reflection of point L across point Y. Point M is the midpoint of segment RL. Point E is the reflection of point M across point I. Find the distance between points L and E. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.5", "dataset": "MATH"}
{"messages": [{"content": "Let CN = 11. Let L be the reflection of point C across point N. Let W be the rotation of point N by angle pi/12 around point C. Let V be the perpendicular bisector of segment WL. Let Y be the midpoint of segment CW. Let S be the reflection of point N across point W. Line U is the reflection of line V across point N. Point K is the intersection of line U and segment SY. What is the length of segment KL? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.52", "dataset": "MATH"}
{"messages": [{"content": "Let GI = 8. Let F be the midpoint of segment GI. Let X be the rotation of point F by angle pi/12 around point I. Point K is obtained by rotating point F by angle 11pi/12 about point X. Let Y be the angle bisector of angle IXK. Point W is the midpoint of segment GK. Let E be the line through point K parallel to line Y. Point R is the intersection of segment GI and line E. Find the distance between points R and W. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "XH = 10. Let M be the midpoint of segment HX. Let B be the rotation of point M by angle pi around point H. Let I be the rotation of point H by angle pi/2 around point B. Line J passes through points I and X. Point D is the midpoint of segment MX. Point S is the reflection of point B across line J. Let Z be the reflection of point D across point I. Find the distance between points S and Z. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.53", "dataset": "MATH"}
{"messages": [{"content": "QH = 11. Let D be the line through points H and Q. Point C is the reflection of point H across point Q. Let R be the vector from point Q to point C. Let J be point C translated by vector R. Let Z be the rotation of point H by angle pi/6 around point J. Let W be the angle bisector of angle HCZ. Point E is the reflection of point Z across point J. Line X passes through points E and C. Line U is the reflection of line X across line D. Point P is the reflection of point Z across line W. Point N is the reflection of point P across line U. What is the length of segment ZN? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33.63", "dataset": "MATH"}
{"messages": [{"content": "Let RQ = 7. Point T is obtained by rotating point Q by angle pi/3 about point R. Point Y is the reflection of point R across point Q. Point B is the midpoint of segment YQ. Let S be the rotation of point R by angle pi/3 around point Y. Let E be the reflection of point S across point Q. Let D be the midpoint of segment TB. Let J be the midpoint of segment DR. Let C be the angle bisector of angle TJB. Let W be the line through point E parallel to line C. Point A is the reflection of point B across segment QT. Point F is the reflection of point R across line W. Find the length of segment FA. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.89", "dataset": "MATH"}
{"messages": [{"content": "PU = 11. Let B be the line through points U and P. Let S be the reflection of point P across point U. Point F is obtained by rotating point U by angle pi/2 about point P. Let L be the perpendicular bisector of segment SF. Line D is the reflection of line L across line B. Let W be the rotation of point U by angle 11pi/12 around point S. Let K be the reflection of point P across point S. Point T is the reflection of point W across segment KF. Point E is the intersection of segment KF and line D. Find the distance between points T and E. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32.25", "dataset": "MATH"}
{"messages": [{"content": "XT = 1. Let H be the perpendicular bisector of segment TX. Let D be the midpoint of segment TX. Point P lies on line H at distance 7 from point X. Line I is the angle bisector of angle TDP. Point Z is the reflection of point X across line I. Let U be the midpoint of segment ZP. Let C be the midpoint of segment TD. Let J be the midpoint of segment UD. Let R be the reflection of point C across point U. Let A be the line through point R parallel to line I. Point B is the intersection of line A and segment PT. What is the length of segment BJ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "EJ = 6. Point H is obtained by rotating point J by angle 5pi/12 about point E. Let N be the rotation of point J by angle pi around point E. Point I is the reflection of point H across segment NJ. Point Z is the midpoint of segment JI. Point V is the reflection of point E across point I. Let D be the reflection of point Z across point V. Point K is the reflection of point D across point I. What is the distance between points V and K? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.43", "dataset": "MATH"}
{"messages": [{"content": "IE = 4. Let P be the reflection of point I across point E. Let A be the rotation of point I by angle 11pi/12 around point E. Let F be the vector from point I to point A. Let V be the perpendicular bisector of segment IP. Point B is the translation of point E by vector F. Point U is obtained by rotating point B by angle pi about point I. Point X is the reflection of point A across line V. Point M is the midpoint of segment XI. Point Y is the midpoint of segment UM. Let W be the reflection of point Y across point E. Find the distance between points W and M. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.83", "dataset": "MATH"}
{"messages": [{"content": "ZH = 2. Point Q is the midpoint of segment HZ. Let N be the midpoint of segment HQ. Let O be the midpoint of segment QN. Point P is obtained by rotating point Z by angle 3pi/4 about point N. Let T be the reflection of point O across point N. Point D is the reflection of point Q across point H. Let V be the line through points O and N. Line F passes through point D perpendicular to line V. Let J be the reflection of line F through point P. Let A be the line through points P and N. Let K be the reflection of point T across point O. Point E is the intersection of lines A and J. Point S is the midpoint of segment KE. What is the distance between points T and S? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.44", "dataset": "MATH"}
{"messages": [{"content": "IM = 4. Line F passes through points I and M. Let IL = 11. Point D is the reflection of point L across line F. Line H is the angle bisector of angle DIM. Point Z is the reflection of point D across line H. Let T be the reflection of point Z across point I. Line P passes through point T perpendicular to line F. Point K is the reflection of point Z across line P. Point B is the midpoint of segment KI. Find the distance between points K and B. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.5", "dataset": "MATH"}
{"messages": [{"content": "Let ZP = 11. Line O is the perpendicular bisector of segment PZ. Point R is the reflection of point P across point Z. Point H is the reflection of point R across line O. Point E is on line O with |EP| = 4. Let Y be the vector from point Z to point E. Point I is the translation of point P by vector Y. Let M be the line through point H perpendicular to segment EI. Point V is the reflection of point I across segment EP. Point U is the reflection of point Z across line M. Let D be the midpoint of segment VU. Find the length of segment ZD. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26.64", "dataset": "MATH"}
{"messages": [{"content": "MZ = 11. Let X be the midpoint of segment ZM. Let G be the reflection of point M across point Z. Let O be the midpoint of segment XZ. Point L is the midpoint of segment ZG. What is the distance between points O and L? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.25", "dataset": "MATH"}
{"messages": [{"content": "FH = 8. Let L be the rotation of point H by angle 5pi/12 around point F. Line D passes through points H and F. Let I be the midpoint of segment HL. Point J is the reflection of point L across line D. Point N is the reflection of point J across segment IL. Point X is the midpoint of segment IL. Find the distance between points X and N. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.6", "dataset": "MATH"}
{"messages": [{"content": "MU = 3. Let E be the rotation of point U by angle 7pi/12 around point M. Point Q is the midpoint of segment UM. Point R is obtained by rotating point E by angle 7pi/12 about point U. Line W passes through point R parallel to segment UQ. Line Z is the reflection of line W across point U. Let N be the midpoint of segment UE. Point H is the reflection of point U across line Z. What is the distance between points H and N? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.59", "dataset": "MATH"}
{"messages": [{"content": "Let DZ = 4. Point T is the midpoint of segment DZ. Point E is the reflection of point Z across point D. Line J is the angle bisector of angle DTE. Line H passes through point Z perpendicular to line J. Let Q be the rotation of point T by angle pi/12 around point D. Let L be the angle bisector of angle QDE. Line A is the reflection of line H across line L. Let O be the line through points Q and E. Point U is the reflection of point E across line L. Point K is the intersection of lines O and A. Point V is the reflection of point K across point U. Let Y be the midpoint of segment QT. Find the distance between points V and Y. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.07", "dataset": "MATH"}
{"messages": [{"content": "LG = 12. Line V is the perpendicular bisector of segment GL. Point S is on line V. Line X passes through point S perpendicular to line V. Let P be the rotation of point G by angle 7pi/12 around point L. Point A is the reflection of point P across segment GL. Line W passes through point G perpendicular to line X. Point K is the reflection of point A across line W. Let B be the reflection of point P across point K. Let M be the reflection of point K across point B. Point C is the reflection of point M across segment PS. What is the distance between points C and P? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114.24", "dataset": "MATH"}
{"messages": [{"content": "EO = 4. Let R be the perpendicular bisector of segment OE. Point Y lies on line R at distance 11 from point O. Let K be the midpoint of segment EY. Let C be the reflection of point Y across point E. Point T is the reflection of point K across point O. Let L be the midpoint of segment YO. Let D be the line through points C and T. Point B is the reflection of point L across line D. Point Z is the reflection of point L across point B. Find the distance between points Z and T. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34.49", "dataset": "MATH"}
{"messages": [{"content": "Let DY = 11. Let H be the vector from point D to point Y. Let U be the perpendicular bisector of segment YD. Point M lies on segment YD. Line X is the perpendicular bisector of segment YM. Let E be the line through point Y perpendicular to segment YD. Line L passes through point D parallel to line E. Line S is the reflection of line U across point Y. Let F be the reflection of point D across point Y. Point A is the midpoint of segment YD. Line B is the reflection of line S across line L. Point P is the midpoint of segment AY. Let G be the line through point P parallel to line X. Let Z be the rotation of point P by angle 7pi/12 around point D. Point O is the reflection of point P across line S. Point J is on line B with |JO| = 8. Let W be the reflection of line G through point J. Let N be point P translated by vector H. Point V is the reflection of point Y across point D. Point K lies on line W at distance 3 from point V. Point T is the reflection of point V across segment NK. Let Q be the line through point Z parallel to line U. Point I is the intersection of segment YT and line Q. What is the length of segment IF? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.2", "dataset": "MATH"}
{"messages": [{"content": "Let IZ = 4. Let P be the rotation of point Z by angle 2pi/3 around point I. Let E be the midpoint of segment ZP. Point K is obtained by rotating point P by angle pi about point I. Let T be the rotation of point I by angle 5pi/6 around point E. Point F is the midpoint of segment TK. Let O be the midpoint of segment IF. Let A be the angle bisector of angle IZO. Let G be the reflection of point P across point F. Point Q is the reflection of point G across line A. What is the distance between points O and Q? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.96", "dataset": "MATH"}
{"messages": [{"content": "Let MK = 6. Line S is the perpendicular bisector of segment KM. Let F be the line through point K parallel to line S. Point D is the midpoint of segment KM. Point N is the reflection of point M across line F. Point Q is the reflection of point D across point M. Let E be the rotation of point N by angle pi/2 around point Q. Point U is obtained by rotating point K by angle pi/12 about point N. Let A be the line through point U perpendicular to line F. Line J is the reflection of line A across point Q. Point L is the reflection of point K across line J. Let Y be the reflection of point E across point N. What is the distance between points L and Y? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.73", "dataset": "MATH"}
{"messages": [{"content": "Let TK = 9. Point Z is the midpoint of segment TK. Point I is obtained by rotating point T by angle pi/6 about point K. Point L is the midpoint of segment IZ. Let R be the rotation of point T by angle 3pi/4 around point Z. Line O passes through points I and T. Let N be the reflection of point T across point I. Let Y be the midpoint of segment NR. Line M is the reflection of line O across point Y. Point S is the reflection of point I across line M. Find the length of segment SL. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.16", "dataset": "MATH"}
{"messages": [{"content": "Let DL = 11. Line J is the perpendicular bisector of segment DL. Let H be the midpoint of segment LD. Point B is on line J with |BL| = 4. Let O be the vector from point D to point L. Point W is the reflection of point D across point L. Let E be the line through point W parallel to line J. Point I is the translation of point H by vector O. Point P is the reflection of point D across line E. Line N passes through points I and B. Point K is the midpoint of segment PW. Let C be the reflection of line E across line N. Line M passes through point B perpendicular to line J. Point Y is the intersection of segment KB and line C. Point S is the reflection of point W across line M. What is the distance between points S and Y? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.3", "dataset": "MATH"}
{"messages": [{"content": "VO = 11. Line M is the perpendicular bisector of segment OV. Let F be the reflection of line M through point V. Line Y passes through point O parallel to line F. Point H is obtained by rotating point O by angle 5pi/6 about point V. Let R be the reflection of point H across point O. Let P be the midpoint of segment OR. Line C is the perpendicular bisector of segment RO. Let S be the reflection of point V across point P. Let E be the reflection of line M across line C. Point G is the reflection of point P across point S. Lines E and Y intersect at point Z. What is the distance between points Z and G? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68.6", "dataset": "MATH"}
{"messages": [{"content": "Let RL = 7. Let J be the reflection of point R across point L. Line U is the perpendicular bisector of segment LR. Let M be the reflection of line U through point J. Line E passes through points R and L. Point N is the intersection of lines E and M. Point I is the midpoint of segment JN. Let H be the midpoint of segment JI. Find the distance between points H and I. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.62", "dataset": "MATH"}
{"messages": [{"content": "Let TO = 7. Let A be the reflection of point O across point T. Let E be the vector from point T to point O. Let D be the midpoint of segment TO. Point G is obtained by rotating point O by angle 11pi/12 about point D. Let C be point D translated by vector E. Point U is the reflection of point A across point D. Let F be the rotation of point U by angle 7pi/12 around point C. Let Q be the angle bisector of angle ADG. Line I is the angle bisector of angle OAG. Let V be the reflection of point A across point O. Point J is the reflection of point C across line I. Point L is the reflection of point J across line Q. Point M is the midpoint of segment FV. What is the distance between points M and L? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.02", "dataset": "MATH"}
{"messages": [{"content": "UR = 5. Let A be the vector from point U to point R. Point Z is the midpoint of segment UR. Let T be point Z translated by vector A. Let O be the rotation of point R by angle pi around point T. Let J be the perpendicular bisector of segment OZ. Let B be the rotation of point U by angle pi/4 around point T. Line C passes through points O and B. Let Q be the reflection of line C across line J. Lines Q and C intersect at point D. Let V be the midpoint of segment TO. Find the length of segment VD. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.57", "dataset": "MATH"}
{"messages": [{"content": "Let OP = 7. Point Z is the reflection of point P across point O. Point Q is obtained by rotating point Z by angle pi/3 about point O. Let M be the reflection of point P across point Q. Line C is the perpendicular bisector of segment PQ. Point T is on line C. Let V be the rotation of point T by angle pi/2 around point Q. Point Y is the reflection of point M across point V. Line K passes through point Y perpendicular to segment MP. Line E passes through point V parallel to line K. Point X is the reflection of point Y across line E. What is the length of segment XZ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.16", "dataset": "MATH"}
{"messages": [{"content": "KG = 4. Point N is the reflection of point G across point K. Point Z is the midpoint of segment KN. Point J is obtained by rotating point N by angle pi/2 about point Z. Let E be the rotation of point K by angle pi/4 around point G. Line L passes through point Z parallel to segment JE. Line L and segment GJ intersect at point A. What is the length of segment NA? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.44", "dataset": "MATH"}
{"messages": [{"content": "CZ = 4. M is placed 10 units away from Z. Let V be the reflection of point M across point C. Let Q be the midpoint of segment ZM. Let E be the midpoint of segment ZV. Let R be the midpoint of segment VQ. Find the length of segment ER. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Let YQ = 7. Point T is obtained by rotating point Y by angle 7pi/12 about point Q. Line O is the angle bisector of angle TYQ. Point R is the midpoint of segment QT. Point Z is the reflection of point R across point T. Point E is the reflection of point R across line O. Let F be the reflection of point E across point Z. Find the length of segment FT. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.62", "dataset": "MATH"}
{"messages": [{"content": "Let XQ = 3. Let E be the midpoint of segment QX. Point P is the midpoint of segment XE. Let V be the vector from point Q to point E. Point U is obtained by rotating point X by angle 2pi/3 about point Q. Point J is obtained by rotating point X by angle pi/6 about point U. Let B be the reflection of point P across point U. Point O is the translation of point U by vector V. Let F be the reflection of point B across point O. Point L is the midpoint of segment PQ. Point S is the reflection of point L across point F. Line N is the angle bisector of angle BFJ. Point Z is the reflection of point O across line N. Find the distance between points S and Z. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.73", "dataset": "MATH"}
{"messages": [{"content": "FR = 12. Let G be the line through points F and R. Point D is on line G with |DF| = 12. Let B be the midpoint of segment DF. Let C be the rotation of point B by angle pi/3 around point D. Let K be the rotation of point B by angle pi/12 around point D. Point L is obtained by rotating point C by angle 7pi/12 about point B. Let H be the midpoint of segment KC. Let X be the reflection of point H across point C. Point N is the midpoint of segment HB. Point T is the reflection of point X across point N. Point M is the reflection of point L across point T. What is the length of segment XM? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.43", "dataset": "MATH"}
{"messages": [{"content": "LR = 8. Let H be the midpoint of segment RL. Let W be the angle bisector of angle HLR. Point F is obtained by rotating point H by angle 5pi/6 about point L. Let M be the reflection of line W through point F. Let K be the rotation of point H by angle pi/3 around point R. Let V be the reflection of line W across line M. Point D is the midpoint of segment KL. Line T passes through points R and D. Lines V and T intersect at point A. Let J be the reflection of point K across point A. Find the distance between points J and D. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57.26", "dataset": "MATH"}
{"messages": [{"content": "OH = 12. Point A is obtained by rotating point H by angle 11pi/12 about point O. Point W is obtained by rotating point O by angle 5pi/12 about point A. Point N is the midpoint of segment AH. Point X is the reflection of point W across segment AH. Let E be the reflection of point N across point A. Find the distance between points X and E. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.87", "dataset": "MATH"}
{"messages": [{"content": "Let IV = 8. Let R be the reflection of point I across point V. Let J be the perpendicular bisector of segment VR. Point N is the reflection of point I across line J. Let G be the midpoint of segment IV. Find the distance between points G and N. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.0", "dataset": "MATH"}
{"messages": [{"content": "EP = 4. Let H be the reflection of point P across point E. Point C is obtained by rotating point H by angle 5pi/12 about point E. Line T is the angle bisector of angle CEP. Line J is the reflection of line T across point C. Point U is on line J with |UC| = 12. Let W be the midpoint of segment CE. Point D is the reflection of point U across point W. Point I is the reflection of point H across segment CE. Point Z is the midpoint of segment EI. Let Q be the midpoint of segment DI. What is the length of segment ZQ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.21", "dataset": "MATH"}
{"messages": [{"content": "Let EZ = 9. Let A be the rotation of point E by angle pi/12 around point Z. Let X be the vector from point Z to point E. Let T be the angle bisector of angle ZEA. Let W be the reflection of line T through point A. Let K be the perpendicular bisector of segment AZ. Line N passes through point E perpendicular to line T. Let C be the reflection of line K across line W. Let J be point E translated by vector X. Let Y be the line through point J parallel to line N. Point B is the reflection of point E across line Y. Line S is the reflection of line N across point A. Point U is the reflection of point B across line S. Point V is the intersection of lines C and Y. Find the length of segment VU. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31.58", "dataset": "MATH"}
{"messages": [{"content": "SG = 12. Let W be the midpoint of segment GS. Let X be the rotation of point W by angle pi/6 around point S. Point T is obtained by rotating point S by angle 2pi/3 about point G. Let V be the midpoint of segment SX. Let A be the reflection of point T across point G. Point J is the midpoint of segment VA. Point U is the midpoint of segment SJ. What is the length of segment JU? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.67", "dataset": "MATH"}
{"messages": [{"content": "EM = 1. Point D is the reflection of point E across point M. Point I is obtained by rotating point M by angle pi/6 about point E. Point N is the reflection of point D across point I. Let B be the line through points N and E. Let A be the midpoint of segment MI. Let F be the line through point A parallel to segment MD. Lines F and B intersect at point Q. Let G be the line through point Q perpendicular to segment MD. Let W be the reflection of line B across line G. Point V is the reflection of point D across line W. Find the length of segment IV. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.9", "dataset": "MATH"}
{"messages": [{"content": "Let GQ = 8. Let V be the rotation of point Q by angle 7pi/12 around point G. Let N be the reflection of point Q across point G. Let P be the rotation of point Q by angle 5pi/12 around point G. Let S be the angle bisector of angle PVN. Point E is the reflection of point G across line S. Point I is the midpoint of segment VN. Point C is the midpoint of segment IP. Point K is the midpoint of segment EP. Point W is the intersection of segments CN and KI. Find the length of segment PW. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.69", "dataset": "MATH"}
{"messages": [{"content": "EQ = 10. Point O is obtained by rotating point Q by angle 2pi/3 about point E. Point K is the reflection of point Q across point E. Point V is the reflection of point O across point E. Point D is the midpoint of segment KO. Let A be the line through point V perpendicular to segment VD. Point L is the reflection of point D across line A. What is the distance between points D and L? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36.06", "dataset": "MATH"}
{"messages": [{"content": "Let QW = 3. Let X be the reflection of point Q across point W. Let M be the midpoint of segment XW. Point J is obtained by rotating point Q by angle pi/6 about point M. Line F is the angle bisector of angle XWQ. Let B be the midpoint of segment WM. Point I is the reflection of point J across line F. Let C be the reflection of point B across point I. What is the distance between points C and J? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.82", "dataset": "MATH"}
{"messages": [{"content": "Let TC = 2. Point Y is the reflection of point C across point T. Let E be the line through points T and C. Line H passes through point C perpendicular to line E. Point M is obtained by rotating point C by angle pi/12 about point T. Let W be the midpoint of segment MY. Point B is the reflection of point M across point C. Point V is the reflection of point B across line H. Point G is the midpoint of segment VW. Find the distance between points B and G. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.18", "dataset": "MATH"}
{"messages": [{"content": "DF = 6. Point T is the midpoint of segment DF. Let J be the midpoint of segment TD. Point P is the midpoint of segment FJ. Let N be the rotation of point F by angle pi/4 around point T. Point W is obtained by rotating point T by angle 5pi/12 about point P. Let Q be the midpoint of segment PN. Point L is the reflection of point Q across point J. Let A be the reflection of point J across point L. Point R is the reflection of point L across point A. Point B is the reflection of point L across segment TW. What is the distance between points B and R? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.4", "dataset": "MATH"}
{"messages": [{"content": "BW = 11. Let P be the midpoint of segment WB. Let Z be the rotation of point P by angle 11pi/12 around point B. Let H be the angle bisector of angle ZWB. Point E is obtained by rotating point P by angle 3pi/4 about point Z. Point T is on line H. Point I is the midpoint of segment BT. Point O is the reflection of point P across line H. Point G is the reflection of point O across point I. Let A be the reflection of line H through point G. Point Y is the reflection of point B across segment EZ. Point U is the reflection of point W across line A. Find the length of segment YU. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.23", "dataset": "MATH"}
{"messages": [{"content": "Let SM = 5. Let A be the rotation of point M by angle pi/3 around point S. Let W be the vector from point A to point M. Point B is the midpoint of segment SM. Point U is obtained by rotating point B by angle 5pi/12 about point S. Let F be point M translated by vector W. Let Q be the perpendicular bisector of segment MS. Point P is obtained by rotating point M by angle 7pi/12 about point B. Point L is the reflection of point P across point F. Let J be the midpoint of segment BM. Point E is the reflection of point L across line Q. Let Y be the midpoint of segment JU. What is the distance between points Y and E? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.06", "dataset": "MATH"}
{"messages": [{"content": "Let PM = 12. Line A is the perpendicular bisector of segment MP. Let B be the line through point M parallel to line A. Let L be the reflection of line B across line A. Point S is the reflection of point M across line L. Let W be the midpoint of segment SP. Let E be the rotation of point W by angle 5pi/6 around point M. Point X is the midpoint of segment EP. Let Y be the midpoint of segment XW. Point U is the midpoint of segment MY. Find the distance between points U and Y. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.2", "dataset": "MATH"}
{"messages": [{"content": "VS = 10. Line M is the perpendicular bisector of segment VS. Point J is obtained by rotating point V by angle pi/4 about point S. Let X be the rotation of point S by angle pi/6 around point V. Let I be the rotation of point S by angle pi/3 around point X. Let Y be the reflection of point I across point V. Let D be the reflection of point J across point X. Line N is the reflection of line M across point D. Point K is the midpoint of segment YS. Point W is the reflection of point Y across line N. Let C be the midpoint of segment IK. What is the length of segment WC? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55.5", "dataset": "MATH"}
{"messages": [{"content": "Let BN = 12. Point K is obtained by rotating point B by angle pi/3 about point N. Line J is the angle bisector of angle NBK. Point T is the reflection of point B across point N. Let C be the reflection of line J through point T. Point X is the reflection of point N across line C. Let Q be the midpoint of segment KX. Find the length of segment TQ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.0", "dataset": "MATH"}
{"messages": [{"content": "VS = 11. Let X be the midpoint of segment VS. Point H is obtained by rotating point X by angle pi/6 about point S. Point O is the midpoint of segment VH. Point M is obtained by rotating point O by angle 3pi/4 about point X. Point Z is obtained by rotating point X by angle pi/3 about point S. Let Q be the line through points Z and M. Let N be the line through point X perpendicular to line Q. Point I is the reflection of point Z across line N. Let U be the midpoint of segment ZS. What is the distance between points U and I? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.44", "dataset": "MATH"}
{"messages": [{"content": "VO = 5. Point U is the midpoint of segment VO. Let C be the rotation of point V by angle pi/4 around point U. Let P be the rotation of point C by angle 3pi/4 around point O. Point F is obtained by rotating point C by angle pi/12 about point V. Line T is the angle bisector of angle PCF. Let S be the perpendicular bisector of segment VP. Point A is the reflection of point O across line S. Line Z is the reflection of line S across line T. Let D be the midpoint of segment AP. Point M is the intersection of segment FA and line Z. Point Y is the reflection of point P across segment FA. Point L is the reflection of point D across point M. Let W be the midpoint of segment YV. What is the length of segment WL? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.51", "dataset": "MATH"}
{"messages": [{"content": "PJ = 9. Point M is obtained by rotating point J by angle pi/2 about point P. Let T be the perpendicular bisector of segment PJ. Let L be the line through point M parallel to line T. Let W be the midpoint of segment MJ. Line R passes through point W parallel to segment PJ. Point O is the intersection of lines R and L. What is the measure of angle PWO, in radians? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.79", "dataset": "MATH"}
{"messages": [{"content": "JH = 8. Let F be the rotation of point H by angle 5pi/6 around point J. Point K is obtained by rotating point J by angle 5pi/6 about point F. Point M is obtained by rotating point K by angle pi/3 about point H. Point D is the midpoint of segment HM. Let T be the reflection of point F across point D. Point Y is the reflection of point T across point K. What is the distance between points D and Y? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48.78", "dataset": "MATH"}
{"messages": [{"content": "AM = 9. Point O is obtained by rotating point M by angle 7pi/12 about point A. AL = 9. Let F be the rotation of point A by angle 11pi/12 around point O. Let T be the line through points A and O. Line P passes through point F parallel to line T. Point K is the reflection of point A across line P. Point H is the reflection of point L across line P. Find the distance between points H and K. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.0", "dataset": "MATH"}
{"messages": [{"content": "MP = 1. Line J is the perpendicular bisector of segment PM. Point D is on line J with |DP| = 2. Point O is obtained by rotating point P by angle pi/3 about point D. Let G be the vector from point P to point O. Let N be the reflection of point O across point P. Let Q be the line through points N and M. Point H is the translation of point D by vector G. Let A be the rotation of point H by angle pi around point O. Let W be the midpoint of segment AM. Point L is the reflection of point H across line Q. Let K be the perpendicular bisector of segment LW. Line F is the reflection of line K across point P. Point S is the reflection of point A across line F. What is the length of segment SW? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.66", "dataset": "MATH"}
{"messages": [{"content": "QS = 2. Let V be the rotation of point Q by angle 7pi/12 around point S. Point D is the reflection of point V across segment QS. Point Z is the reflection of point D across point S. Point C is the midpoint of segment QS. Let X be the midpoint of segment CZ. Point J is the reflection of point X across segment QS. Find the distance between points J and X. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.93", "dataset": "MATH"}
{"messages": [{"content": "YE = 6. Let T be the reflection of point E across point Y. Let W be the reflection of point E across point T. Point R is obtained by rotating point Y by angle 3pi/4 about point W. Line C passes through points R and W. Let K be the perpendicular bisector of segment TE. Line L is the reflection of line K across line C. Line M passes through point T parallel to line C. Lines M and L intersect at point I. Find the length of segment IY. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.63", "dataset": "MATH"}
{"messages": [{"content": "Let FQ = 12. Point I is obtained by rotating point Q by angle 2pi/3 about point F. Let U be the reflection of point F across point Q. Line E is the perpendicular bisector of segment FI. Point G is the reflection of point Q across line E. Line Z is the angle bisector of angle UFQ. Let V be the rotation of point F by angle pi/4 around point U. Point H is the midpoint of segment VQ. Let L be the line through point U perpendicular to line Z. Let O be the rotation of point I by angle 11pi/12 around point V. Point M is the reflection of point O across line Z. Let T be the midpoint of segment HM. Line D passes through point T perpendicular to line L. Point X is the reflection of point Q across line D. Find the distance between points X and G. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.22", "dataset": "MATH"}
{"messages": [{"content": "Let HF = 9. Line S is the perpendicular bisector of segment FH. Point I is obtained by rotating point H by angle pi about point F. Let R be the vector from point H to point I. Line G is the angle bisector of angle HFI. Let A be the midpoint of segment FH. Let J be point I translated by vector R. Point Y lies on line G at distance 2 from point H. Let N be the reflection of point Y across point F. Let D be the angle bisector of angle NJF. Line B is the reflection of line D across point A. Point P is the translation of point Y by vector R. Let Z be the reflection of line S through point F. Let K be the midpoint of segment IY. Point O is the intersection of lines B and Z. Point V is the reflection of point O across point P. What is the length of segment KV? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.04", "dataset": "MATH"}
{"messages": [{"content": "Let AP = 5. Point M is the midpoint of segment AP. Let X be the midpoint of segment AM. Let O be the rotation of point X by angle pi/3 around point M. Line S is the perpendicular bisector of segment OX. Line W is the angle bisector of angle XAM. Point C is the reflection of point A across line S. Let T be the vector from point M to point P. Point Q is the translation of point O by vector T. Let H be the line through point P perpendicular to line W. Point I is the midpoint of segment MX. Let B be the reflection of point A across point I. Point Y is the reflection of point Q across line H. Point F is the reflection of point Y across point B. What is the distance between points F and C? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.31", "dataset": "MATH"}
{"messages": [{"content": "Let RH = 2. Point S is the reflection of point H across point R. Let C be the midpoint of segment RS. Let I be the rotation of point R by angle 2pi/3 around point C. Let E be the reflection of point R across point S. Point G is the reflection of point I across point C. Let A be the midpoint of segment GC. Let N be the angle bisector of angle ECI. Let D be the midpoint of segment HI. Let Q be the line through point R parallel to line N. Segment AD and line Q intersect at point U. Find the length of segment GU. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.01", "dataset": "MATH"}
{"messages": [{"content": "Let NY = 12. Point M is the reflection of point Y across point N. Point C is the midpoint of segment NM. Point J is the reflection of point M across point Y. Line O passes through point N perpendicular to segment NM. Point Q is obtained by rotating point Y by angle pi/3 about point C. Let Z be the line through point Q parallel to line O. Line H passes through point C perpendicular to segment NM. Point W is the reflection of point J across line H. Point D is the reflection of point W across line Z. Find the distance between points D and C. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60.0", "dataset": "MATH"}
{"messages": [{"content": "Let KW = 12. Line A is the perpendicular bisector of segment KW. Let P be the rotation of point K by angle pi/4 around point W. Line Z is the angle bisector of angle PKW. Line T is the reflection of line A across line Z. Line Y passes through point W parallel to line A. Let M be the midpoint of segment KP. Point J is the intersection of lines T and Y. What is the length of segment MJ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.6", "dataset": "MATH"}
{"messages": [{"content": "SE = 4. Point H is the reflection of point E across point S. Let I be the rotation of point S by angle 11pi/12 around point H. Point A is the midpoint of segment SE. Point C is the reflection of point I across segment HE. Point P is the midpoint of segment CA. Let T be the reflection of point P across point I. Point D is the midpoint of segment TI. What is the distance between points C and D? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.77", "dataset": "MATH"}
{"messages": [{"content": "IA = 4. Let G be the rotation of point I by angle 5pi/12 around point A. Point E is the midpoint of segment AI. Let L be the angle bisector of angle GAE. Point Q is obtained by rotating point G by angle pi/3 about point E. Let C be the rotation of point Q by angle pi/3 around point A. Line N is the perpendicular bisector of segment AI. Let S be the line through points E and C. Let Y be the line through point Q perpendicular to line L. Let R be the reflection of line N across line Y. Point K is the intersection of lines R and S. Point X is the reflection of point G across line R. What is the distance between points K and X? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.57", "dataset": "MATH"}
{"messages": [{"content": "KY = 5. Let O be the perpendicular bisector of segment KY. Line X passes through point K parallel to line O. Let D be the rotation of point Y by angle pi/12 around point K. Point S is the reflection of point D across line X. Point A is the reflection of point D across line O. Point I is the reflection of point D across point A. Let U be the reflection of point Y across point I. Point T is the reflection of point U across point A. What is the distance between points S and T? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.19", "dataset": "MATH"}
{"messages": [{"content": "Let NF = 1. Let R be the midpoint of segment FN. Point Y is obtained by rotating point F by angle 7pi/12 about point R. Point Q is the midpoint of segment YR. Point E is the reflection of point F across segment NY. Find the length of segment QE. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "JR = 12. Let K be the midpoint of segment RJ. Line A is the perpendicular bisector of segment RK. Point W lies on line A at distance 1 from point R. Line E passes through point K perpendicular to segment RJ. Let C be the reflection of point J across point W. Line V is the reflection of line E across line A. Let G be the reflection of line A across line E. Let X be the angle bisector of angle WRK. Let L be the reflection of line X through point C. Point Y is on line G. Line Z passes through point Y parallel to line L. Point O is the intersection of lines V and Z. Find the distance between points O and Y. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.12", "dataset": "MATH"}
{"messages": [{"content": "Let BE = 11. Let G be the line through points B and E. Let P be the line through point B perpendicular to line G. Point N lies on line P at distance 7 from point E. Let X be the reflection of point N across point B. Point I is the reflection of point E across point X. Let W be the midpoint of segment IB. Point Q is the reflection of point W across segment XI. What is the length of segment QW? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.91", "dataset": "MATH"}
{"messages": [{"content": "Let EY = 7. Let S be the midpoint of segment EY. Let K be the vector from point S to point Y. Line X is the perpendicular bisector of segment YS. Point H is the translation of point Y by vector K. Point Z is on line X with |ZH| = 9. Let L be the midpoint of segment SZ. Let F be the midpoint of segment HZ. Let U be the midpoint of segment HL. Find the distance between points F and U. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.29", "dataset": "MATH"}
{"messages": [{"content": "SB = 9. Point W is the midpoint of segment SB. Let P be the midpoint of segment BW. Line V is the perpendicular bisector of segment SW. Line Y is the reflection of line V across point W. Let D be the reflection of point S across point P. Point I lies on line Y at distance 9 from point W. Let M be the line through point S parallel to segment DI. Let A be the midpoint of segment DI. Point L is the reflection of point A across line M. What is the distance between points W and L? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.4", "dataset": "MATH"}
{"messages": [{"content": "Let QC = 9. Let I be the reflection of point C across point Q. Let B be the rotation of point Q by angle 5pi/6 around point I. Let G be the midpoint of segment BI. Let H be the reflection of point I across point B. Let S be the angle bisector of angle BQC. Point R is obtained by rotating point H by angle pi/4 about point C. Point U is the reflection of point R across segment BI. Let D be the midpoint of segment GU. Point Y is the reflection of point U across line S. Let M be the midpoint of segment YG. Find the length of segment MD. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
{"messages": [{"content": "JH = 10. Let B be the midpoint of segment HJ. Point T is obtained by rotating point H by angle 5pi/6 about point J. Let V be the midpoint of segment TB. Let I be the rotation of point T by angle pi/3 around point J. Point D is the midpoint of segment HV. Let W be the midpoint of segment IJ. Line C is the angle bisector of angle BDW. Let G be the line through point D perpendicular to line C. Point M is the reflection of point W across line G. Find the length of segment MW. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.57", "dataset": "MATH"}
{"messages": [{"content": "OP = 7. Let A be the vector from point O to point P. Point F is the translation of point P by vector A. Point M is the translation of point F by vector A. Let W be the rotation of point M by angle 2pi/3 around point P. Point L is the midpoint of segment FW. Let S be the midpoint of segment LP. Segments WP and OS intersect at point B. What is the length of segment FB? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.74", "dataset": "MATH"}
{"messages": [{"content": "OF = 9. Point H is obtained by rotating point O by angle 5pi/6 about point F. Line A is the angle bisector of angle FHO. Point X is the reflection of point O across line A. Line C passes through point H perpendicular to line A. Point G is the reflection of point X across line C. Let T be the midpoint of segment GX. Point I is the reflection of point H across segment GX. Find the distance between points I and T. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
{"messages": [{"content": "DR = 11. Line F is the perpendicular bisector of segment RD. Let W be the midpoint of segment RD. Line I is the perpendicular bisector of segment WD. Point P is on line I with |PW| = 6. Point Z is the midpoint of segment PD. Point V is the midpoint of segment WZ. Let A be the line through point Z perpendicular to line F. Point X is the reflection of point R across line A. Point C is the midpoint of segment XV. Point K is the reflection of point Z across line F. What is the length of segment CK? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.52", "dataset": "MATH"}
{"messages": [{"content": "Let WC = 10. Let D be the reflection of point C across point W. Let A be the perpendicular bisector of segment CD. Point Q is obtained by rotating point W by angle 7pi/12 about point C. Point H is obtained by rotating point D by angle pi/4 about point Q. Point J is obtained by rotating point W by angle 5pi/6 about point C. Let X be the midpoint of segment HC. Line I is the perpendicular bisector of segment JX. Point F is the reflection of point Q across line A. Let T be the reflection of line I across line A. Point G is the intersection of line T and segment FC. Point M is the reflection of point G across line A. Find the length of segment MJ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.71", "dataset": "MATH"}
{"messages": [{"content": "FH = 3. Line B passes through point F perpendicular to segment HF. Point K is the reflection of point H across line B. Point L is the midpoint of segment HF. Line Q is the perpendicular bisector of segment HF. Let R be the rotation of point F by angle 5pi/12 around point K. Line M passes through point R perpendicular to line Q. Let P be the midpoint of segment LR. Let V be the rotation of point H by angle 11pi/12 around point K. Point Y is the midpoint of segment FR. Segments FR and VP intersect at point W. Line C passes through point Y parallel to line M. Point U is the reflection of point L across line C. Point D is the reflection of point W across point U. Find the length of segment RD. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.5", "dataset": "MATH"}
{"messages": [{"content": "ZY = 7. Point W is obtained by rotating point Y by angle 5pi/12 about point Z. Let T be the angle bisector of angle ZWY. Point L is the reflection of point Z across line T. Point S is the midpoint of segment LZ. Let R be the midpoint of segment WS. Point U is the midpoint of segment RZ. Line M passes through point R perpendicular to segment WU. Point A is the reflection of point S across line M. Find the distance between points A and W. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.96", "dataset": "MATH"}
{"messages": [{"content": "LZ = 8. Let F be the rotation of point L by angle pi/2 around point Z. Point X is the midpoint of segment FL. Point V is obtained by rotating point F by angle pi/3 about point Z. Let W be the perpendicular bisector of segment XL. Point R is the midpoint of segment ZF. Point D lies on line W at distance 6 from point L. Point T is the reflection of point R across segment VL. Let Q be the reflection of point T across point D. Let M be the midpoint of segment RV. Point I is the reflection of point M across segment XQ. What is the length of segment IX? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.46", "dataset": "MATH"}
{"messages": [{"content": "Let RQ = 4. Let X be the rotation of point Q by angle 7pi/12 around point R. Point O is obtained by rotating point R by angle pi/4 about point Q. Point V is the reflection of point O across point X. Point F is obtained by rotating point X by angle pi/12 about point O. Let P be the rotation of point F by angle 11pi/12 around point Q. Point N is the midpoint of segment QO. Let I be the reflection of point F across point X. Let B be the reflection of point P across point F. Let A be the midpoint of segment BI. Segments NF and VO intersect at point W. What is the length of segment WA? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.99", "dataset": "MATH"}
{"messages": [{"content": "RG = 11. Point U is the reflection of point R across point G. Let P be the rotation of point U by angle 5pi/6 around point G. Point Q is the reflection of point P across segment GR. Let B be the midpoint of segment GQ. Point M is obtained by rotating point B by angle pi/2 about point U. Point H is the reflection of point U across point M. Line A passes through point M parallel to segment GR. Let Y be the line through points G and H. Point D is the intersection of lines A and Y. What is the length of segment DP? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.71", "dataset": "MATH"}
{"messages": [{"content": "Let SI = 12. Point L is obtained by rotating point S by angle pi/12 about point I. Let B be the reflection of point S across point L. Let M be the midpoint of segment BL. Point T is the reflection of point M across segment SI. Find the length of segment TM. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.32", "dataset": "MATH"}
{"messages": [{"content": "DV = 1. Line H is the perpendicular bisector of segment VD. Line N passes through point V parallel to line H. Point S is on line N with |SV| = 11. Point Z lies on line H at distance 1 from point D. Point I is the reflection of point Z across point D. Point E is on line N with |ES| = 8. Let Q be the reflection of point E across point Z. Let Y be the reflection of point Q across point I. Line A passes through points E and Z. Point P is the reflection of point Y across segment VD. Point U is the reflection of point P across line A. Find the length of segment UQ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.24", "dataset": "MATH"}
{"messages": [{"content": "Let AX = 3. Point F is the reflection of point A across point X. Let Z be the rotation of point X by angle pi/2 around point F. Let M be the vector from point Z to point A. Let D be point X translated by vector M. Let Y be the rotation of point D by angle 7pi/12 around point A. Let N be point Y translated by vector M. Point B is the midpoint of segment NZ. Let J be the perpendicular bisector of segment AZ. Line W passes through point B parallel to line J. Let P be the rotation of point A by angle 2pi/3 around point B. Point E is the reflection of point P across line W. Point T is the reflection of point E across segment YB. Segments PX and AZ intersect at point R. Find the length of segment RT. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.41", "dataset": "MATH"}
{"messages": [{"content": "Let LI = 9. Point B is obtained by rotating point I by angle 5pi/6 about point L. Let Q be the rotation of point I by angle 2pi/3 around point B. Point V is the midpoint of segment BQ. Point R is the reflection of point V across point Q. Let F be the angle bisector of angle VQI. Line Y is the perpendicular bisector of segment VQ. Let D be the reflection of point R across point B. Let U be the reflection of line F across line Y. Let S be the reflection of point D across point L. Point N is the midpoint of segment SV. Line A is the reflection of line Y across line U. Point H is the reflection of point R across line A. Point C is the reflection of point N across line A. Point T is the reflection of point H across point D. Point W is the reflection of point T across segment DC. What is the length of segment WV? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66.76", "dataset": "MATH"}
{"messages": [{"content": "Let NO = 12. Point C is the reflection of point O across point N. Let L be the midpoint of segment ON. Let D be the rotation of point C by angle 11pi/12 around point O. Let A be the reflection of point L across point O. Let V be the angle bisector of angle DLA. Point S is the reflection of point L across point N. Point H is the reflection of point S across line V. Point I is the reflection of point H across point L. What is the distance between points D and I? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.84", "dataset": "MATH"}
{"messages": [{"content": "Let LJ = 3. Point G is obtained by rotating point J by angle 11pi/12 about point L. Let U be the reflection of point G across point J. Point X is obtained by rotating point J by angle 7pi/12 about point U. Let F be the vector from point J to point X. Let H be point L translated by vector F. Let V be point G translated by vector F. Point A is obtained by rotating point V by angle pi/12 about point U. Line K passes through points H and V. Point M is the reflection of point X across line K. Point S is the intersection of segments AJ and LX. Point C is the reflection of point M across segment AJ. Find the distance between points S and C. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.72", "dataset": "MATH"}
{"messages": [{"content": "Let TP = 10. Let Q be the line through point T perpendicular to segment PT. Let M be the rotation of point T by angle pi/4 around point P. Let V be the rotation of point P by angle pi/4 around point T. Let C be the midpoint of segment PT. Point D is the reflection of point M across line Q. Let I be the line through point C perpendicular to segment VM. Let X be the reflection of point M across point D. Point H is the reflection of point X across line I. Find the length of segment XH. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.32", "dataset": "MATH"}
{"messages": [{"content": "Let OB = 4. Line X is the perpendicular bisector of segment OB. Line G passes through point O perpendicular to line X. Point Z lies on line X. Point R is the reflection of point Z across point O. Point D is the reflection of point R across line G. What is the distance between points D and Z? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "JI = 2. Line R passes through points J and I. Let P be the reflection of point I across point J. Let H be the rotation of point I by angle 11pi/12 around point J. Point Z is obtained by rotating point I by angle pi/6 about point J. Point S is obtained by rotating point H by angle pi/3 about point I. Line D is the angle bisector of angle PJS. Let O be the reflection of line R across line D. Let Q be the line through point P parallel to line O. Point C is the reflection of point I across line Q. Find the length of segment ZC. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.6", "dataset": "MATH"}
{"messages": [{"content": "RS = 8. Let Y be the midpoint of segment SR. Let L be the rotation of point Y by angle pi/6 around point S. Point N is the reflection of point Y across point R. Point V is the midpoint of segment LN. Point Q is the reflection of point S across point L. Point Z is the midpoint of segment VQ. Find the length of segment ZR. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.59", "dataset": "MATH"}
{"messages": [{"content": "Let DS = 3. Let W be the rotation of point S by angle 2pi/3 around point D. Point N is the midpoint of segment DS. Let H be the angle bisector of angle WNS. Point P is the reflection of point N across point S. Point J is the reflection of point P across line H. Point R is the reflection of point S across point P. What is the distance between points J and R? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.05", "dataset": "MATH"}
{"messages": [{"content": "Let WM = 11. Point Y is the midpoint of segment WM. Let P be the perpendicular bisector of segment MW. Point B is the midpoint of segment WY. Point Q is on line P. Point R is the midpoint of segment BQ. Point N is the midpoint of segment QR. Let F be the rotation of point N by angle pi/3 around point W. Point E is the reflection of point F across segment RW. Let K be the line through points E and W. Point H is the reflection of point Y across line K. Point I is the midpoint of segment WH. Find the length of segment IH. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.75", "dataset": "MATH"}
{"messages": [{"content": "SM = 9. Point J is the midpoint of segment SM. Line E is the perpendicular bisector of segment SM. Let D be the line through point M parallel to line E. Point V is the reflection of point J across line D. Find the distance between points J and V. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.0", "dataset": "MATH"}
{"messages": [{"content": "AN = 1. Let I be the rotation of point N by angle 7pi/12 around point A. Let X be the angle bisector of angle NAI. Point S is the reflection of point I across point N. Line J passes through points S and A. Let K be the rotation of point A by angle pi around point N. Line R is the reflection of line X across line J. Point W is obtained by rotating point S by angle pi/4 about point I. Point Y is the midpoint of segment IN. Let H be the reflection of line X through point I. Lines H and R intersect at point B. Point U is the reflection of point K across segment YB. Find the distance between points W and U. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.36", "dataset": "MATH"}
{"messages": [{"content": "Let FG = 10. Line A is the perpendicular bisector of segment GF. Let P be the vector from point F to point G. Point U is the midpoint of segment GF. Let E be point U translated by vector P. Point D is the reflection of point E across line A. Line Q is the reflection of line A across point F. Point W is obtained by rotating point D by angle 5pi/6 about point F. Point X is the reflection of point G across line Q. Point N is the reflection of point D across point W. Let V be the reflection of line Q through point E. Point K is the reflection of point N across line V. Let T be the reflection of point D across point K. Point I is the midpoint of segment TG. Line S passes through point K perpendicular to segment EI. Point R is the reflection of point N across line S. What is the length of segment XR? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118.92", "dataset": "MATH"}
{"messages": [{"content": "Let OV = 6. Point L is obtained by rotating point O by angle pi/6 about point V. Let G be the reflection of point V across point O. Let T be the midpoint of segment LG. Line S is the angle bisector of angle TGL. Point J is the reflection of point V across line S. Point R is the reflection of point L across segment OV. What is the distance between points J and R? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.93", "dataset": "MATH"}
{"messages": [{"content": "YB = 10. Point M is the midpoint of segment YB. Let K be the reflection of point M across point Y. Line R is the perpendicular bisector of segment YM. Line E is the reflection of line R across point M. Point H is the reflection of point K across line E. Find the distance between points Y and H. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.0", "dataset": "MATH"}
{"messages": [{"content": "Let GC = 12. Line E is the perpendicular bisector of segment GC. Point I is the reflection of point G across point C. Point Q is the reflection of point C across point I. Let B be the reflection of point G across point Q. Point Y is the reflection of point B across line E. Let O be the rotation of point G by angle pi/12 around point Y. Let X be the midpoint of segment OG. Let K be the reflection of point X across point B. Point A is the midpoint of segment BX. Let F be the midpoint of segment KQ. What is the distance between points A and F? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55.57", "dataset": "MATH"}
{"messages": [{"content": "Let VK = 1. Let G be the perpendicular bisector of segment KV. Let Z be the line through point V perpendicular to line G. Let J be the rotation of point K by angle pi/4 around point V. Point Y is the reflection of point K across point J. Line A is the angle bisector of angle YVJ. Point C is the reflection of point Y across line A. Let Q be the reflection of point V across point J. Let N be the reflection of point C across point K. Let F be the reflection of point J across point Q. Point P is the reflection of point N across line Z. Point I is the reflection of point K across point F. Point S is the reflection of point I across line Z. Find the distance between points S and P. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.76", "dataset": "MATH"}
{"messages": [{"content": "Let MA = 2. Point D is the midpoint of segment MA. Let L be the rotation of point M by angle 5pi/12 around point A. Line O passes through points A and L. Let H be the rotation of point M by angle 5pi/12 around point D. Point E is the reflection of point M across line O. Point Q is the reflection of point L across segment EH. Point Z is the midpoint of segment EH. What is the length of segment ZQ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.21", "dataset": "MATH"}
{"messages": [{"content": "Let DV = 12. Let K be the reflection of point V across point D. Line W is the angle bisector of angle VDK. Point E lies on line W at distance 8 from point D. Point L is the reflection of point E across segment DV. Point B is the reflection of point D across point K. Point Z is the midpoint of segment BK. Let O be the midpoint of segment BZ. Find the distance between points L and O. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.47", "dataset": "MATH"}
{"messages": [{"content": "Let VB = 2. Point Z is obtained by rotating point B by angle pi/2 about point V. Let T be the reflection of point V across point Z. Point E is the reflection of point B across point Z. Point M is obtained by rotating point E by angle pi/3 about point B. Point H is the reflection of point T across segment ZM. Point Y is the midpoint of segment HB. Point G is the reflection of point Z across segment VB. Find the distance between points Y and G. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.61", "dataset": "MATH"}
{"messages": [{"content": "EM = 7. Let G be the rotation of point M by angle pi/3 around point E. Let L be the reflection of point M across point E. Point F is the midpoint of segment MG. Let I be the midpoint of segment LG. Point W is the midpoint of segment ME. Point H is the midpoint of segment GI. Point C is the reflection of point W across point G. What is the measure of angle CFH, in radians? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.05", "dataset": "MATH"}
{"messages": [{"content": "NV = 8. Point Y is obtained by rotating point N by angle pi/3 about point V. Point E is the reflection of point Y across point N. Let T be the midpoint of segment EV. Let I be the midpoint of segment VN. Let B be the reflection of point N across point T. What is the length of segment BI? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.93", "dataset": "MATH"}
{"messages": [{"content": "Let AW = 8. Point C is obtained by rotating point W by angle pi/6 about point A. Point V is the midpoint of segment WC. Let J be the reflection of point W across point C. Let M be the midpoint of segment AJ. Let G be the rotation of point W by angle 7pi/12 around point A. Line E is the perpendicular bisector of segment GC. Line F passes through point V parallel to line E. Line B passes through points W and M. Point P is the intersection of lines F and B. Find the distance between points C and P. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.19", "dataset": "MATH"}
{"messages": [{"content": "Let GB = 8. Let N be the vector from point B to point G. Point T is the midpoint of segment GB. Point H is the reflection of point T across point G. Let L be the rotation of point B by angle pi/2 around point T. Point Q is the reflection of point G across point L. Let Y be point H translated by vector N. Let J be the midpoint of segment LY. Point M is the midpoint of segment YQ. Let E be the midpoint of segment JM. Find the length of segment HE. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.16", "dataset": "MATH"}
{"messages": [{"content": "YR = 5. Let W be the perpendicular bisector of segment RY. Let Z be the reflection of point R across point Y. Point N lies on line W at distance 9 from point Y. Point B is the reflection of point Y across point N. Let S be the midpoint of segment ZN. Line P is the perpendicular bisector of segment SB. Point X is the reflection of point R across line P. Let F be the midpoint of segment BX. Find the length of segment XF. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.85", "dataset": "MATH"}
{"messages": [{"content": "LG = 8. Let T be the vector from point G to point L. Point E is the midpoint of segment GL. Let N be point E translated by vector T. Point M is on segment GL. Line R passes through point G perpendicular to segment GL. Point I is the midpoint of segment NM. Point X is the reflection of point I across line R. Point S is the reflection of point I across point L. Find the distance between points X and S. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.0", "dataset": "MATH"}
{"messages": [{"content": "HS = 1. Let X be the midpoint of segment SH. Let L be the rotation of point H by angle 11pi/12 around point S. Let N be the line through point S perpendicular to segment SH. Let D be the reflection of point L across point X. Let W be the midpoint of segment DS. Point J is the reflection of point L across line N. What is the distance between points W and J? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "Let MQ = 6. Point R is obtained by rotating point M by angle 7pi/12 about point Q. Let A be the angle bisector of angle QRM. Let P be the reflection of point M across point R. Let Z be the reflection of line A through point P. Let C be the midpoint of segment QR. Point X is the reflection of point C across line Z. What is the length of segment XR? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.63", "dataset": "MATH"}
{"messages": [{"content": "OV = 3. Let U be the rotation of point O by angle pi/3 around point V. Point H is obtained by rotating point V by angle 5pi/6 about point U. Let E be the perpendicular bisector of segment HV. Let L be the midpoint of segment VU. Point J is the reflection of point L across line E. Point Z is the midpoint of segment LJ. Point I is the midpoint of segment OU. Let G be the rotation of point U by angle 11pi/12 around point Z. Let M be the reflection of point H across point L. Line B is the angle bisector of angle GZH. Point A is the midpoint of segment MO. Let W be the line through point L parallel to line B. Line W and segment VI intersect at point N. What is the distance between points N and A? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.47", "dataset": "MATH"}
{"messages": [{"content": "Let FT = 4. Let B be the rotation of point F by angle pi/6 around point T. Let X be the reflection of point B across point F. Let S be the rotation of point F by angle 3pi/4 around point X. Let R be the midpoint of segment FB. Let W be the rotation of point X by angle pi around point R. Point V is the reflection of point X across segment TF. Let N be the rotation of point B by angle 5pi/12 around point T. Point M is the reflection of point W across segment TF. Point C is the midpoint of segment MT. Let P be the rotation of point N by angle pi/2 around point S. Let K be the midpoint of segment BV. Let H be the reflection of point S across point P. Segments CK and TF intersect at point J. Find the length of segment JH. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.42", "dataset": "MATH"}
{"messages": [{"content": "JX = 11. Point T is the reflection of point X across point J. Line A passes through points J and X. Line Q passes through point X perpendicular to line A. Let V be the rotation of point T by angle pi/3 around point J. Point U is the reflection of point V across line Q. Let F be the reflection of point T across point X. Point K is the midpoint of segment UJ. Point Z is the reflection of point F across point U. What is the length of segment KZ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.5", "dataset": "MATH"}
{"messages": [{"content": "Let HM = 11. Let F be the rotation of point H by angle pi/12 around point M. Let B be the vector from point F to point M. Point X is the translation of point M by vector B. Point U is obtained by rotating point H by angle 7pi/12 about point X. Point G is the reflection of point H across point M. Let Y be the reflection of point U across point G. Let S be the line through points X and Y. Point I is the reflection of point Y across point H. Point P is the reflection of point I across line S. What is the length of segment FP? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62.69", "dataset": "MATH"}
{"messages": [{"content": "ET = 4. Let A be the rotation of point E by angle pi/6 around point T. Point K is obtained by rotating point E by angle pi/12 about point A. Let C be the line through point E perpendicular to segment TE. Point S is the reflection of point A across line C. Let J be the reflection of point A across point K. Let Y be the midpoint of segment JS. Let D be the line through point E parallel to segment JS. Point L is the midpoint of segment TY. Point X is the reflection of point Y across line D. Find the distance between points X and L. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
{"messages": [{"content": "Let ZJ = 7. Let U be the rotation of point Z by angle pi/4 around point J. Line C is the perpendicular bisector of segment JZ. Point W is the reflection of point U across line C. Let L be the line through point U parallel to line C. Line D is the reflection of line C across point U. Let F be the reflection of point U across point W. Line M is the perpendicular bisector of segment JF. Segment ZJ and line D intersect at point X. Segment ZJ and line L intersect at point K. Let S be the line through point F perpendicular to segment ZJ. Line R is the reflection of line M across line S. Point N is obtained by rotating point J by angle 2pi/3 about point U. Let E be the line through point N parallel to segment ZJ. Let T be the reflection of point K across point Z. Let H be the angle bisector of angle UXT. Point I is the intersection of line R and segment FJ. Point G is the reflection of point I across line H. Segment WX and line E intersect at point Y. Point B is the midpoint of segment YF. Let V be the line through points B and X. Point P is the reflection of point G across line V. What is the distance between points Y and P? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.1", "dataset": "MATH"}
{"messages": [{"content": "WT = 9. Point L is obtained by rotating point T by angle 7pi/12 about point W. Let P be the perpendicular bisector of segment TW. Point Z is the reflection of point L across point T. Let Q be the line through point L parallel to line P. Point H is the reflection of point T across point Z. Let K be the line through points H and Z. Point Y is the reflection of point W across line K. Point N is the reflection of point H across line Q. What is the length of segment YN? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50.28", "dataset": "MATH"}
{"messages": [{"content": "Let RO = 8. Let W be the rotation of point O by angle 5pi/12 around point R. Let C be the vector from point R to point O. Let A be point O translated by vector C. Line E passes through points A and R. Let U be the midpoint of segment WO. Line V passes through point A parallel to segment OW. Line X is the reflection of line E across line V. Point N is the reflection of point U across line X. What is the length of segment AN? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.63", "dataset": "MATH"}
{"messages": [{"content": "LQ = 10. Point R is the midpoint of segment QL. Let P be the rotation of point R by angle 5pi/6 around point L. Point S is the reflection of point P across point R. Point Z is the reflection of point P across point L. Line E passes through points S and P. Let V be the line through point Z parallel to line E. Let Y be the reflection of line V across line E. Point N is the reflection of point S across line Y. What is the length of segment ZN? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.39", "dataset": "MATH"}
{"messages": [{"content": "UD = 6. Point B is obtained by rotating point D by angle pi/3 about point U. Point T is the midpoint of segment UD. Point J is obtained by rotating point T by angle 7pi/12 about point D. Let L be the midpoint of segment DJ. Point A is the midpoint of segment BU. Line Q passes through point D parallel to segment BU. Point X is the reflection of point A across point L. Point H is the reflection of point J across line Q. What is the distance between points X and H? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.44", "dataset": "MATH"}
{"messages": [{"content": "KW = 7. Let C be the rotation of point W by angle 5pi/6 around point K. Point N is the midpoint of segment WK. Let V be the midpoint of segment CN. Point M is the reflection of point V across segment WK. Let E be the reflection of point M across point V. Find the length of segment EN. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.1", "dataset": "MATH"}
{"messages": [{"content": "UK = 4. Point L is the midpoint of segment UK. Let Q be the line through point K perpendicular to segment KL. Point H is the reflection of point U across line Q. Point V is the midpoint of segment KL. What is the distance between points V and H? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.0", "dataset": "MATH"}
{"messages": [{"content": "SB = 6. Point V is the midpoint of segment SB. Let W be the perpendicular bisector of segment VB. Let E be the rotation of point S by angle pi/2 around point V. Let N be the angle bisector of angle EVB. Point F is the midpoint of segment SV. Point H is on line W with |HS| = 6. Line K is the angle bisector of angle HFS. Let A be the midpoint of segment EV. Let R be the reflection of line K across line N. Line D is the perpendicular bisector of segment VE. Point Y is the reflection of point V across line R. Line I is the reflection of line D across point Y. Point U is the reflection of point F across line I. Find the length of segment UA. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.27", "dataset": "MATH"}
{"messages": [{"content": "Let JN = 7. Line Y passes through point N perpendicular to segment JN. Point E is the midpoint of segment JN. Point H is the midpoint of segment EN. Let X be the reflection of point E across point J. Point P is the midpoint of segment XJ. Point C is the midpoint of segment PE. Let W be the line through point C parallel to line Y. Point U lies on line W. Point Z is the reflection of point P across point H. Let A be the angle bisector of angle UZX. Point T is the reflection of point C across line A. What is the length of segment TZ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.38", "dataset": "MATH"}
{"messages": [{"content": "CJ = 1. Let O be the reflection of point C across point J. Point W is the reflection of point O across point C. Point F is the midpoint of segment CJ. Let L be the rotation of point O by angle 5pi/12 around point W. Let G be the midpoint of segment CF. Point Z is the reflection of point F across segment LG. Point N is the reflection of point Z across segment CJ. Find the length of segment ZN. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.29", "dataset": "MATH"}
{"messages": [{"content": "Let VS = 6. Let J be the rotation of point V by angle pi/6 around point S. Line H is the perpendicular bisector of segment SJ. Point U is the reflection of point V across line H. Let W be the rotation of point U by angle 3pi/4 around point J. Let Q be the rotation of point W by angle 7pi/12 around point V. Let Y be the midpoint of segment JU. Let D be the reflection of line H through point W. Point A is the reflection of point Q across segment SJ. Point G is the reflection of point A across line D. Find the distance between points G and Y. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35.72", "dataset": "MATH"}
{"messages": [{"content": "QK = 4. Line I is the perpendicular bisector of segment QK. Point R is the midpoint of segment QK. Let Z be the rotation of point K by angle 5pi/6 around point Q. Let S be the reflection of point R across point Z. Point Y is the reflection of point Z across line I. Point U is the reflection of point Y across segment SQ. Find the length of segment RU. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.06", "dataset": "MATH"}
{"messages": [{"content": "Let SV = 2. Let G be the reflection of point S across point V. Point W is the midpoint of segment GV. Let N be the perpendicular bisector of segment SG. Point R is the reflection of point W across line N. Find the distance between points G and R. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Let TG = 7. Point X is the midpoint of segment GT. Let N be the rotation of point G by angle pi/12 around point X. Point M is the reflection of point N across point X. Let O be the line through points N and X. Line V passes through point T perpendicular to line O. Let K be the reflection of point T across point M. Point Y is the reflection of point M across line V. What is the distance between points K and Y? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.97", "dataset": "MATH"}
{"messages": [{"content": "Let JN = 4. Point W is obtained by rotating point N by angle pi/2 about point J. Point C is the reflection of point N across point W. Let O be the midpoint of segment JN. Point R is the midpoint of segment OC. Let Z be the perpendicular bisector of segment RN. Let M be the line through point W parallel to line Z. Line M and segment OC intersect at point Q. Point I is the midpoint of segment QC. Point F is the reflection of point N across segment OW. What is the length of segment FI? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.89", "dataset": "MATH"}
{"messages": [{"content": "Let FT = 11. Let U be the perpendicular bisector of segment TF. Let G be the rotation of point F by angle 5pi/12 around point T. Let M be the midpoint of segment GF. Let L be the reflection of line U through point T. Point J is the reflection of point G across line U. Let P be the midpoint of segment TG. Let E be the line through point P perpendicular to line L. Let H be the line through point G parallel to line E. Let B be the perpendicular bisector of segment GF. Let W be the rotation of point J by angle 11pi/12 around point G. Let V be the reflection of line B across line H. Point I is the reflection of point T across line V. Let Y be the reflection of point M across point W. Point X is the reflection of point Y across point I. Find the distance between points X and P. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59.01", "dataset": "MATH"}
{"messages": [{"content": "SK = 5. Let L be the perpendicular bisector of segment SK. Point J is on line L with |JK| = 9. Point P is the reflection of point J across segment SK. Point F is the midpoint of segment SK. Let E be the reflection of point P across point J. Let T be the midpoint of segment FK. Let I be the line through points S and E. Point C is the reflection of point P across point K. Point Y is the reflection of point T across line I. Find the distance between points Y and C. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.94", "dataset": "MATH"}
{"messages": [{"content": "Let WL = 2. Point U is obtained by rotating point W by angle 3pi/4 about point L. Point E is obtained by rotating point U by angle pi/12 about point L. Point I is the midpoint of segment WL. Point Q is the midpoint of segment LE. Line F passes through point L perpendicular to segment WL. Point R is the reflection of point I across line F. What is the length of segment QR? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.52", "dataset": "MATH"}
{"messages": [{"content": "IW = 3. Let K be the rotation of point W by angle pi/4 around point I. Point C is obtained by rotating point K by angle 5pi/12 about point W. Point B is the reflection of point W across segment IK. Point J is the midpoint of segment KC. Let O be the reflection of point B across point C. Let S be the reflection of point O across point J. Find the length of segment OS. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.02", "dataset": "MATH"}
{"messages": [{"content": "FD = 12. Let H be the midpoint of segment FD. Point P is the midpoint of segment FH. Let I be the rotation of point D by angle 2pi/3 around point P. Let L be the line through point I parallel to segment DF. Point Z is the midpoint of segment IH. Point J is the reflection of point Z across line L. Point R is the reflection of point D across segment JI. Let E be the midpoint of segment ZD. What is the distance between points R and E? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25.48", "dataset": "MATH"}
{"messages": [{"content": "FA = 9. Let H be the rotation of point F by angle 5pi/12 around point A. Point Y is the midpoint of segment AH. Point D is the midpoint of segment AY. Let N be the reflection of point F across point D. Point I is the midpoint of segment AN. Point K is the reflection of point I across segment ND. What is the length of segment NK? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.48", "dataset": "MATH"}
{"messages": [{"content": "HW = 3. Point S is obtained by rotating point H by angle 2pi/3 about point W. Let E be the perpendicular bisector of segment WS. Let U be the rotation of point S by angle 11pi/12 around point W. Let D be the reflection of point U across point W. Let X be the reflection of line E through point U. Point G is the midpoint of segment DH. Point L is the reflection of point D across line X. Find the length of segment GL. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.21", "dataset": "MATH"}
{"messages": [{"content": "LZ = 11. Let O be the rotation of point L by angle 5pi/6 around point Z. Let T be the rotation of point O by angle 5pi/6 around point Z. Point U is the midpoint of segment OZ. Let G be the line through point T perpendicular to segment OZ. Let S be the midpoint of segment TO. Line K passes through point S parallel to line G. Point R is the midpoint of segment US. Point D is the reflection of point R across line K. Find the distance between points D and S. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.75", "dataset": "MATH"}
{"messages": [{"content": "Let DY = 9. Point L is obtained by rotating point Y by angle 7pi/12 about point D. Let R be the midpoint of segment YD. Let G be the perpendicular bisector of segment RL. Point F is the reflection of point Y across line G. Point E is the reflection of point F across segment YD. Point M is the reflection of point F across point E. Find the length of segment MD. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39.22", "dataset": "MATH"}
{"messages": [{"content": "PM = 9. Point B is the midpoint of segment PM. Line T is the perpendicular bisector of segment MB. Line O passes through point P parallel to line T. Point A is obtained by rotating point B by angle pi/6 about point M. Point Q is the midpoint of segment PA. Point G is the midpoint of segment AB. Point K is the reflection of point Q across line O. Line W is the perpendicular bisector of segment AP. Let Y be the line through point K parallel to line W. Point U is the reflection of point G across line O. Point D is the reflection of point U across segment AP. Point N is the reflection of point D across line Y. What is the distance between points N and B? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Let IQ = 7. Point O is the midpoint of segment QI. Let R be the midpoint of segment OQ. Let D be the reflection of point R across point O. Let X be the line through point Q perpendicular to segment QR. Point B is the reflection of point R across line X. Let F be the midpoint of segment QB. Find the distance between points F and D. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.12", "dataset": "MATH"}
{"messages": [{"content": "RD = 5. Line F is the perpendicular bisector of segment DR. Point B is on line F with |BD| = 1. Line Y is the perpendicular bisector of segment BD. Point Q is the midpoint of segment BR. Point U is the reflection of point R across line Y. Let N be the midpoint of segment BQ. Point V is the midpoint of segment DR. Line J is the reflection of line Y across point N. Point P is the reflection of point Q across line J. Point S is the intersection of segment PV and line J. What is the distance between points S and U? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.03", "dataset": "MATH"}
{"messages": [{"content": "Let XY = 3. Let G be the perpendicular bisector of segment XY. Point U is obtained by rotating point X by angle 5pi/6 about point Y. Let F be the midpoint of segment XU. Point A is the reflection of point U across line G. Let T be the vector from point F to point X. Let W be point X translated by vector T. Point E is the reflection of point X across point W. Point P is the translation of point A by vector T. Point J is the reflection of point F across line G. Let Z be the line through points U and P. Let V be the line through point E parallel to segment JY. Point M is the intersection of lines V and Z. What is the length of segment WM? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.51", "dataset": "MATH"}
{"messages": [{"content": "Let DU = 4. Point B is the midpoint of segment UD. Point S is the midpoint of segment BD. Point G is the reflection of point S across point U. Let W be the rotation of point S by angle 7pi/12 around point G. Point K is the midpoint of segment GW. Let O be the rotation of point D by angle 11pi/12 around point U. Point E is obtained by rotating point K by angle 7pi/12 about point O. Let N be the rotation of point O by angle pi/6 around point U. Let Y be the reflection of point U across point N. Point T is the midpoint of segment OG. Let A be the angle bisector of angle YET. Point H is the reflection of point B across line A. What is the length of segment NH? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.8", "dataset": "MATH"}
{"messages": [{"content": "Let IY = 3. Point D is the midpoint of segment YI. Point Z is obtained by rotating point D by angle pi/12 about point Y. Point X is obtained by rotating point Z by angle 3pi/4 about point D. Let K be the midpoint of segment XD. Let Q be the midpoint of segment KI. Point J is the reflection of point X across segment KI. What is the distance between points Q and J? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.96", "dataset": "MATH"}
{"messages": [{"content": "QE = 9. Point L is the reflection of point Q across point E. Let Y be the midpoint of segment QE. Point R is the reflection of point Y across point L. Let O be the reflection of point Q across point R. Point I is the reflection of point E across point O. Point P is the reflection of point E across point R. Find the distance between points P and I. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63.0", "dataset": "MATH"}
{"messages": [{"content": "Let TJ = 8. Point X is the midpoint of segment TJ. Let Q be the rotation of point X by angle 11pi/12 around point J. Let L be the angle bisector of angle XJT. Line P passes through point Q perpendicular to line L. Point C is the reflection of point X across line P. Point F is obtained by rotating point C by angle 7pi/12 about point Q. Let N be the line through point C parallel to line P. Let H be the reflection of point T across point J. Point O is the reflection of point F across line N. Point R is the midpoint of segment OH. What is the length of segment FR? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.82", "dataset": "MATH"}
{"messages": [{"content": "FT = 3. Let M be the reflection of point F across point T. Point A is the midpoint of segment TM. Line K is the perpendicular bisector of segment FM. Point C is the reflection of point F across point A. Line P is the angle bisector of angle CMF. Point D is the reflection of point A across line K. Line G is the perpendicular bisector of segment AF. Point B is obtained by rotating point M by angle 5pi/6 about point D. Line U is the reflection of line G across line K. Let W be the reflection of point B across point F. Point Z is the reflection of point W across line U. Point S is the reflection of point D across line P. What is the length of segment SZ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.85", "dataset": "MATH"}
{"messages": [{"content": "Let GT = 1. Let P be the rotation of point T by angle 3pi/4 around point G. Let I be the reflection of point T across point G. Line L passes through point I perpendicular to segment GP. Point F is the reflection of point T across line L. Line C passes through point T perpendicular to segment GP. Let D be the perpendicular bisector of segment IF. Line W is the reflection of line D across line C. Point U is the reflection of point F across line W. What is the distance between points P and U? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.85", "dataset": "MATH"}
{"messages": [{"content": "Let ZC = 7. Let R be the vector from point Z to point C. Let L be the midpoint of segment ZC. Point M is the reflection of point L across point C. Point P is the reflection of point C across point M. Let Y be the midpoint of segment PM. Let B be point Y translated by vector R. Let D be the perpendicular bisector of segment ZY. Line U passes through point B perpendicular to line D. Point V is obtained by rotating point L by angle 11pi/12 about point P. Point I is the midpoint of segment YV. Let F be the line through point M perpendicular to line U. Point H is the reflection of point B across point Y. Point K is the reflection of point H across line F. Find the length of segment IK. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.8", "dataset": "MATH"}
{"messages": [{"content": "IL = 4. Let T be the rotation of point I by angle 7pi/12 around point L. Point W is the reflection of point L across point I. Let P be the midpoint of segment IW. Let V be the line through points T and P. Point Y is the reflection of point I across line V. What is the distance between points Y and W? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.51", "dataset": "MATH"}
{"messages": [{"content": "PA = 1. Let N be the reflection of point P across point A. Line F is the perpendicular bisector of segment NP. Let O be the reflection of point N across point P. Let I be the reflection of point P across point O. Line V is the perpendicular bisector of segment PO. Let Q be the line through point I parallel to line V. Let J be the rotation of point I by angle pi/3 around point O. Let W be the reflection of line F across line Q. Let B be the midpoint of segment AI. Point L is obtained by rotating point N by angle pi/2 about point O. Line H passes through points J and L. Lines W and H intersect at point D. Point M is the reflection of point P across segment BL. Point T is the midpoint of segment DM. What is the distance between points T and P? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.2", "dataset": "MATH"}
{"messages": [{"content": "Let MP = 6. Let W be the vector from point P to point M. Let A be the line through points P and M. Line F passes through point P perpendicular to line A. Line E passes through point M parallel to line F. Let L be the reflection of point P across point M. Line I is the reflection of line E across line F. Let Y be point L translated by vector W. Let G be the reflection of line F across line I. Point V is the midpoint of segment PY. Point R is on line G with |RV| = 2. Let D be the midpoint of segment LR. Point O is the midpoint of segment YD. Point J is the reflection of point O across segment LR. What is the length of segment YJ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.04", "dataset": "MATH"}
{"messages": [{"content": "DV = 12. Let A be the rotation of point V by angle 11pi/12 around point D. Let R be the rotation of point V by angle pi/2 around point A. Point Z is the midpoint of segment VD. Point T is the midpoint of segment AR. Point N is the midpoint of segment VT. Let O be the midpoint of segment ZN. Point M is the reflection of point O across segment RV. Find the length of segment MO. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.97", "dataset": "MATH"}
{"messages": [{"content": "SL = 6. Point R is obtained by rotating point S by angle 5pi/6 about point L. Let G be the perpendicular bisector of segment SR. Point M is the midpoint of segment SL. Line V passes through point M parallel to line G. Point H is the reflection of point L across line V. Find the distance between points R and H. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.69", "dataset": "MATH"}
{"messages": [{"content": "RE = 9. Let S be the line through points E and R. Let T be the vector from point R to point E. Let L be point E translated by vector T. Point Y is obtained by rotating point R by angle 5pi/6 about point L. Let B be the reflection of point Y across point L. Point P is the reflection of point B across point Y. Let W be the midpoint of segment LE. Point A is the midpoint of segment PW. Point K is the reflection of point A across line S. Point F is the reflection of point A across point K. Let V be the midpoint of segment FB. Let M be the midpoint of segment VB. What is the distance between points M and R? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.47", "dataset": "MATH"}
{"messages": [{"content": "Let AM = 5. Let F be the midpoint of segment MA. Let P be the rotation of point A by angle 5pi/6 around point M. Line W is the perpendicular bisector of segment AF. Line I passes through points M and F. Line L passes through point P parallel to line W. Point R is the reflection of point M across line L. Let Q be the reflection of line W through point F. Lines Q and I intersect at point D. Let K be the midpoint of segment DR. Find the distance between points R and K. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.96", "dataset": "MATH"}
{"messages": [{"content": "Let BV = 7. Let T be the reflection of point B across point V. Let P be the line through points V and T. Line N passes through point T perpendicular to line P. Point Q is the reflection of point B across line N. What is the distance between points Q and T? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.0", "dataset": "MATH"}
{"messages": [{"content": "Let QV = 6. Let B be the reflection of point Q across point V. Point E is obtained by rotating point Q by angle pi about point B. Let U be the midpoint of segment BE. Point T is the reflection of point E across point Q. Let A be the rotation of point U by angle 7pi/12 around point E. Line Y is the perpendicular bisector of segment TU. Let C be the perpendicular bisector of segment EQ. Let D be the reflection of line Y across line C. Point P is the reflection of point A across line D. Point L is the reflection of point A across point U. Find the length of segment LP. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.41", "dataset": "MATH"}
{"messages": [{"content": "Let OK = 5. Let P be the perpendicular bisector of segment OK. Line C is the reflection of line P across point O. Let G be the line through point O parallel to line C. Let H be the line through point K parallel to line P. Let W be the vector from point O to point K. Point F is obtained by rotating point K by angle pi/6 about point O. Point I is the midpoint of segment OK. Point B is the reflection of point F across point I. Let M be point K translated by vector W. Line N passes through points K and B. Line Y is the reflection of line H across line G. Lines Y and N intersect at point L. Let V be the reflection of point L across point I. Point Q is the reflection of point V across point M. Find the distance between points L and Q. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.0", "dataset": "MATH"}
{"messages": [{"content": "YH = 6. Let J be the vector from point H to point Y. Point F is the translation of point Y by vector J. Point D is obtained by rotating point H by angle 7pi/12 about point F. Let W be point D translated by vector J. Point Z is obtained by rotating point F by angle 11pi/12 about point Y. Let S be the vector from point F to point Z. Point N is the translation of point Y by vector S. Let P be the angle bisector of angle HDY. Point R is the reflection of point F across line P. Point Q is the midpoint of segment RW. Point G is the reflection of point Q across segment NW. Point B is the midpoint of segment NW. Find the distance between points G and B. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.88", "dataset": "MATH"}
{"messages": [{"content": "NP = 3. Let R be the vector from point N to point P. Let Y be point P translated by vector R. Line X is the perpendicular bisector of segment NP. Let Q be the line through point Y parallel to line X. Point O is the midpoint of segment PN. Let J be the perpendicular bisector of segment PY. Point V is the reflection of point O across line Q. Point I lies on line J at distance 3 from point V. Let W be the reflection of line Q through point P. Let U be the line through point I parallel to segment PN. Line M is the reflection of line U across point N. Lines M and W intersect at point A. Find the length of segment YA. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.71", "dataset": "MATH"}
{"messages": [{"content": "Let IG = 1. Let C be the perpendicular bisector of segment GI. Let A be the line through point G parallel to line C. Let K be the midpoint of segment IG. Point H is the reflection of point K across point I. Point Y is the reflection of point H across line A. Point L is obtained by rotating point H by angle pi/2 about point G. Point E is the reflection of point Y across segment LH. Let T be the reflection of point G across point E. Point Q is the reflection of point K across segment LH. Find the distance between points Q and T. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.22", "dataset": "MATH"}
{"messages": [{"content": "YW = 4. Let K be the vector from point Y to point W. Let P be point W translated by vector K. Point N is obtained by rotating point Y by angle 3pi/4 about point W. Line D is the perpendicular bisector of segment YP. Point U is the reflection of point Y across point N. Point R is the reflection of point N across line D. Point Z is the midpoint of segment PR. Point T is the reflection of point U across line D. What is the measure of angle TNZ, in radians? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.79", "dataset": "MATH"}
{"messages": [{"content": "KY = 3. Point C is obtained by rotating point K by angle pi/6 about point Y. Point Q is the reflection of point Y across point C. Point D is the reflection of point Y across point Q. Let T be the reflection of point K across point Q. Let W be the midpoint of segment DK. What is the distance between points T and W? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.08", "dataset": "MATH"}
{"messages": [{"content": "Let JT = 4. Point R is obtained by rotating point T by angle 5pi/12 about point J. Line X passes through points T and J. Line O passes through point R parallel to line X. Let A be the midpoint of segment TJ. Let L be the midpoint of segment JR. Point D is the midpoint of segment LT. Let W be the perpendicular bisector of segment DA. Let K be the line through point D perpendicular to line O. Line Y is the reflection of line O across line W. Line P is the reflection of line K across line Y. Point S is the reflection of point L across line P. Find the length of segment AS. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.73", "dataset": "MATH"}
{"messages": [{"content": "CZ = 6. Let X be the midpoint of segment CZ. Point J is the midpoint of segment XC. Let G be the midpoint of segment XJ. Let M be the rotation of point Z by angle pi/12 around point J. Let Q be the midpoint of segment CG. Let D be the midpoint of segment GJ. Let K be the midpoint of segment DZ. Point F is the reflection of point Q across segment MX. Let B be the reflection of point J across point K. What is the distance between points F and B? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.89", "dataset": "MATH"}
{"messages": [{"content": "KP = 1. Point W is obtained by rotating point K by angle pi/6 about point P. Let L be the rotation of point K by angle 5pi/12 around point W. Let S be the angle bisector of angle PWL. Point X lies on line S at distance 8 from point W. Let N be the reflection of point L across point X. Point Q is the reflection of point L across line S. Point Z is the reflection of point K across segment NQ. Find the measure of angle ZPQ, in radians. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.96", "dataset": "MATH"}
{"messages": [{"content": "HD = 5. Point T is obtained by rotating point H by angle pi/6 about point D. Let A be the line through points T and D. Let R be the reflection of point T across point H. Let P be the line through point D perpendicular to line A. Let M be the rotation of point H by angle pi/12 around point D. Point X is the midpoint of segment DR. Point B is the reflection of point X across line P. Line N passes through points X and T. Line Y is the angle bisector of angle XMB. Point U is the reflection of point T across line Y. Point E is the reflection of point H across line N. What is the distance between points E and U? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.94", "dataset": "MATH"}
{"messages": [{"content": "Let IX = 10. Let B be the rotation of point I by angle 3pi/4 around point X. Point Q is obtained by rotating point X by angle pi/3 about point I. Line T is the angle bisector of angle QXB. Point P is the reflection of point I across line T. Point N is the reflection of point X across point B. Let W be the midpoint of segment PI. Let O be the reflection of point W across point N. Point J is the reflection of point O across segment PI. Find the distance between points I and J. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50.37", "dataset": "MATH"}
{"messages": [{"content": "Let JA = 1. Let Y be the rotation of point J by angle pi/4 around point A. Let L be the rotation of point A by angle pi/3 around point J. Point E is obtained by rotating point A by angle pi/6 about point Y. Line Q is the angle bisector of angle EJY. Let R be the rotation of point Y by angle 11pi/12 around point A. Let N be the midpoint of segment LR. Point G is the reflection of point E across point N. Line M passes through point L parallel to line Q. Point X is the reflection of point R across line M. Find the distance between points X and G. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.89", "dataset": "MATH"}
{"messages": [{"content": "Let WZ = 9. Point D is the reflection of point W across point Z. Line Y is the perpendicular bisector of segment ZW. Point A is the midpoint of segment DZ. Let U be the vector from point D to point W. Point T is the reflection of point D across line Y. Point G is the translation of point T by vector U. Point M is the reflection of point A across point W. Let I be the rotation of point G by angle pi/2 around point Z. Point X is obtained by rotating point T by angle 5pi/6 about point M. Point K is the midpoint of segment XI. Let L be the midpoint of segment KD. Point J is the reflection of point D across segment IK. What is the length of segment JL? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41.79", "dataset": "MATH"}
{"messages": [{"content": "Let EQ = 10. Let H be the vector from point Q to point E. Let L be point E translated by vector H. Line B is the perpendicular bisector of segment LQ. Point U is on line B with |UE| = 12. Let R be the angle bisector of angle QLE. Point F is the midpoint of segment UL. Line X is the reflection of line R across point F. Point W is the reflection of point Q across line X. Let T be the reflection of point W across point F. What is the distance between points E and T? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.32", "dataset": "MATH"}
{"messages": [{"content": "Let ZY = 3. Let K be the perpendicular bisector of segment YZ. Point P is on line K. Let T be the rotation of point Z by angle 3pi/4 around point Y. Point F is the reflection of point T across line K. Let L be the midpoint of segment PZ. Line G is the reflection of line K across point L. Point O is the reflection of point T across line G. Find the length of segment OF. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "CA = 7. Line G is the perpendicular bisector of segment CA. Line I is the reflection of line G across point C. Point P is the reflection of point A across line I. Point F is the reflection of point P across line G. Point Y is the reflection of point C across line I. Point M is the midpoint of segment AF. What is the distance between points Y and M? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.0", "dataset": "MATH"}
{"messages": [{"content": "Let SP = 9. Point G is obtained by rotating point P by angle pi/3 about point S. Point U is the midpoint of segment SG. Line W is the angle bisector of angle GPU. Point V is the reflection of point U across line W. Let J be the reflection of point S across point P. Point L is the reflection of point V across segment SP. Line E is the perpendicular bisector of segment SP. Let M be the line through point J perpendicular to segment SP. Point I is the reflection of point U across line M. Let F be the midpoint of segment IP. Let K be the line through point L parallel to line W. Let H be the reflection of line E across line K. Point R is the reflection of point L across line H. Point Z is the reflection of point F across point R. Find the distance between points V and Z. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25.62", "dataset": "MATH"}
{"messages": [{"content": "QL = 6. Point S is obtained by rotating point Q by angle pi/4 about point L. Let E be the midpoint of segment SL. Line I is the angle bisector of angle LQE. Point V lies on segment EQ. Point X is the reflection of point L across segment VS. Point A is the reflection of point S across line I. Point U is the midpoint of segment SA. Point K is the midpoint of segment XA. What is the length of segment KU? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Let ON = 1. Let I be the perpendicular bisector of segment ON. Point T is on line I with |TN| = 8. Let S be the perpendicular bisector of segment NT. Line C passes through point T parallel to line S. Point Y is the reflection of point O across line C. Let X be the reflection of point N across point T. What is the distance between points X and Y? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Let YZ = 8. Let A be the rotation of point Z by angle pi around point Y. Let Q be the reflection of point Y across point Z. Let S be the rotation of point A by angle pi/4 around point Y. Let T be the midpoint of segment AS. Point G is the reflection of point A across point Z. Point D is the reflection of point T across point G. Line R is the angle bisector of angle GQS. Point J is the reflection of point D across line R. Line P is the perpendicular bisector of segment JQ. Point B is the reflection of point Y across line P. What is the distance between points B and J? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.0", "dataset": "MATH"}
{"messages": [{"content": "RX = 5. Let M be the line through points X and R. Let E be the rotation of point X by angle 7pi/12 around point R. Let A be the reflection of point X across point E. Let J be the line through point E perpendicular to line M. Let Z be the midpoint of segment XE. Line V passes through point Z perpendicular to line J. Line L passes through point A parallel to line V. Point I is the reflection of point Z across line L. Let D be the line through points E and I. Lines L and D intersect at point U. Find the distance between points I and U. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.49", "dataset": "MATH"}
{"messages": [{"content": "GY = 1. Line V is the perpendicular bisector of segment YG. Let U be the reflection of line V through point Y. Point F is the reflection of point Y across line U. Line S passes through points G and F. Point M is the midpoint of segment YF. Let N be the vector from point M to point G. Point A lies on line V at distance 12 from point F. Point E is the reflection of point A across line S. Let H be point E translated by vector N. Point R is the midpoint of segment EY. Let Q be the reflection of point H across point M. Point T is the midpoint of segment GR. Point P is the reflection of point A across point Q. Find the distance between points P and T. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.61", "dataset": "MATH"}
{"messages": [{"content": "CA = 5. Point H is the reflection of point A across point C. Line D passes through points C and H. Line V passes through point A perpendicular to line D. Let L be the rotation of point H by angle pi/2 around point C. Point P is obtained by rotating point H by angle pi/3 about point A. Point E is the reflection of point C across line V. Let F be the midpoint of segment HL. Let K be the midpoint of segment CF. Line J passes through point K perpendicular to segment EP. Point W is the reflection of point P across line J. Find the distance between points H and W. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.47", "dataset": "MATH"}
{"messages": [{"content": "Let OG = 5. Line Z passes through points O and G. Let P be the rotation of point O by angle pi/3 around point G. Line S is the perpendicular bisector of segment PO. Point N is the midpoint of segment PG. Let V be the line through point P parallel to line S. Lines Z and V intersect at point T. Find the measure of angle NPT, in radians. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.52", "dataset": "MATH"}
{"messages": [{"content": "SO = 6. Point W is the reflection of point O across point S. Line F is the angle bisector of angle SWO. Let C be the rotation of point W by angle pi/3 around point O. Let U be the midpoint of segment SC. Point R is the reflection of point U across line F. Let Z be the reflection of point U across point R. Point N is the reflection of point O across point Z. Let Q be the line through point Z perpendicular to line F. Point E is the reflection of point N across line Q. What is the length of segment EZ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.7", "dataset": "MATH"}
{"messages": [{"content": "RN = 4. Let Z be the midpoint of segment NR. Point F is obtained by rotating point N by angle pi/2 about point R. Let E be the rotation of point Z by angle 5pi/12 around point R. Let H be the midpoint of segment NZ. Point X is the reflection of point E across point Z. Line Q is the angle bisector of angle XNF. Point T is the midpoint of segment FR. Point D is obtained by rotating point Z by angle 5pi/12 about point H. Let L be the reflection of line Q through point D. Point K is the reflection of point E across line L. Let I be the angle bisector of angle RTD. Let Y be the midpoint of segment ZH. Point W is the reflection of point K across line I. Find the length of segment YW. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.52", "dataset": "MATH"}
{"messages": [{"content": "CN = 10. Line I passes through point C perpendicular to segment CN. Point J is the reflection of point N across line I. Point Z is the midpoint of segment CN. Line E is the perpendicular bisector of segment CN. Let D be the rotation of point N by angle pi/6 around point Z. Point A is the reflection of point D across segment CN. Point Q is the reflection of point A across line E. Line B is the perpendicular bisector of segment JQ. Point R is the reflection of point C across line B. Find the length of segment RJ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.59", "dataset": "MATH"}
{"messages": [{"content": "Let LG = 9. Point Z is the midpoint of segment GL. Let F be the midpoint of segment GZ. Point R is obtained by rotating point F by angle 11pi/12 about point Z. Let B be the vector from point R to point F. Let Q be the midpoint of segment GR. Let X be point Q translated by vector B. Let D be the rotation of point F by angle pi/12 around point Q. Let U be the midpoint of segment GX. Point O is the midpoint of segment LD. Line M passes through point U parallel to segment GL. Line W is the perpendicular bisector of segment GL. Let A be the perpendicular bisector of segment OU. Point N is the reflection of point Q across segment GL. Point J is the reflection of point L across line A. Line I is the reflection of line W across point J. Lines I and M intersect at point Y. What is the length of segment YN? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.65", "dataset": "MATH"}
{"messages": [{"content": "Let OJ = 11. Let B be the midpoint of segment JO. Let V be the midpoint of segment JB. Point K is obtained by rotating point V by angle pi/12 about point J. Point S is the reflection of point V across point O. Let W be the rotation of point O by angle 7pi/12 around point B. Point N is the midpoint of segment SK. Point M is the reflection of point O across point W. Point C is the midpoint of segment NM. Line X passes through point B parallel to segment NM. Line X and segment KM intersect at point H. What is the length of segment CH? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.62", "dataset": "MATH"}
{"messages": [{"content": "GR = 5. Line X is the perpendicular bisector of segment GR. Point A is on line X with |AG| = 7. Line W is the reflection of line X across point R. Let P be the line through point A parallel to segment GR. Point Q is the reflection of point R across line P. Point C is the reflection of point A across segment GR. Line K passes through points C and Q. Line K and segment GR intersect at point B. Let V be the reflection of point Q across point B. Line U passes through point V parallel to line W. Point M is the intersection of line U and segment GR. What is the distance between points Q and M? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.39", "dataset": "MATH"}
{"messages": [{"content": "Let OE = 5. Let F be the rotation of point O by angle 7pi/12 around point E. Point C is the reflection of point F across segment EO. Line Z is the perpendicular bisector of segment FE. Point U is the midpoint of segment OF. Point P is the reflection of point U across segment EO. Let T be the vector from point C to point U. Let S be the line through point E perpendicular to segment EO. Point G is the reflection of point P across line S. Let J be point O translated by vector T. Point A is the reflection of point C across line S. Point N is obtained by rotating point U by angle 3pi/4 about point A. Point V is the reflection of point N across line Z. Point Y is the midpoint of segment VA. Point H is the reflection of point Y across point J. Point K is the reflection of point G across point H. Find the length of segment KH. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26.29", "dataset": "MATH"}
{"messages": [{"content": "Let OM = 2. Let J be the rotation of point O by angle pi/6 around point M. Let Y be the rotation of point J by angle 3pi/4 around point O. Let H be the angle bisector of angle YMJ. Line V is the reflection of line H across point Y. Line P is the reflection of line V across point O. Let Q be the vector from point O to point J. Line X is the reflection of line H across line V. Let R be the reflection of point Y across point M. Line A passes through points J and M. Point B is the translation of point M by vector Q. Let D be the reflection of line A through point R. Point F is the reflection of point B across line P. Lines D and X intersect at point K. Let U be the midpoint of segment FJ. What is the length of segment KU? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.73", "dataset": "MATH"}
{"messages": [{"content": "Let JV = 11. Let S be the vector from point J to point V. Let U be point V translated by vector S. Let L be the rotation of point J by angle 11pi/12 around point U. Let P be the line through points U and L. Point Y is on segment VJ. Point I is the midpoint of segment YU. Point O is the reflection of point I across line P. Find the measure of angle IUO, in radians. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.52", "dataset": "MATH"}
{"messages": [{"content": "YV = 10. Let W be the rotation of point Y by angle 3pi/4 around point V. Let X be the vector from point Y to point W. Point T is the translation of point W by vector X. Let J be the reflection of point W across point Y. Point A is the midpoint of segment VY. Let G be the line through point J perpendicular to segment TA. Line Q is the reflection of line G across point Y. Point B is the midpoint of segment AW. Point K is the reflection of point B across line Q. Point H is the intersection of segment TA and line Q. Find the distance between points H and K. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.99", "dataset": "MATH"}
{"messages": [{"content": "Let BO = 11. Let C be the rotation of point B by angle pi/3 around point O. Point D is obtained by rotating point C by angle pi/12 about point B. Point N is the midpoint of segment OC. Point L is the reflection of point N across point O. Point K is the reflection of point B across segment DL. Point P is the reflection of point O across segment DL. What is the distance between points K and P? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.0", "dataset": "MATH"}
{"messages": [{"content": "Let BI = 5. Point A is the midpoint of segment BI. Let K be the line through point B perpendicular to segment BA. Point N is obtained by rotating point B by angle pi about point I. Point F is the reflection of point N across line K. Line R is the perpendicular bisector of segment BA. Let P be the perpendicular bisector of segment AN. Let Y be the reflection of line P across line R. Let M be the reflection of line P across line Y. Point L is the reflection of point N across line M. What is the distance between points L and F? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.5", "dataset": "MATH"}
{"messages": [{"content": "UE = 12. Point V is obtained by rotating point U by angle 3pi/4 about point E. Point H is the midpoint of segment UE. Let X be the midpoint of segment HV. Let D be the reflection of point X across point H. Find the distance between points D and H. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.39", "dataset": "MATH"}
{"messages": [{"content": "Let DE = 9. Point V is obtained by rotating point E by angle 11pi/12 about point D. Point S is the midpoint of segment VE. Line M is the perpendicular bisector of segment ED. Let Y be the rotation of point V by angle pi/4 around point D. Let Z be the reflection of line M through point V. Point X is the reflection of point E across line Z. Point H is the reflection of point S across segment ED. Let Q be the rotation of point X by angle pi/2 around point H. Point N is the midpoint of segment XQ. Let L be the midpoint of segment YQ. Let U be the reflection of point L across point S. Point W is the reflection of point U across segment ED. What is the distance between points N and W? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31.93", "dataset": "MATH"}
{"messages": [{"content": "Let RO = 3. Let F be the rotation of point R by angle 5pi/12 around point O. Point D is the midpoint of segment FR. Let I be the rotation of point O by angle 5pi/6 around point R. Let N be the midpoint of segment DO. Let Q be the midpoint of segment IR. Let E be the reflection of point I across point N. Line Y is the angle bisector of angle QIE. Point H is the reflection of point N across line Y. Find the length of segment EH. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.19", "dataset": "MATH"}
{"messages": [{"content": "Let PE = 1. Let O be the vector from point P to point E. Line I is the perpendicular bisector of segment PE. Point U is the translation of point E by vector O. Let B be the rotation of point P by angle pi/12 around point E. Point J is the reflection of point U across line I. Let W be the vector from point B to point J. Point V is on line I. Let N be point E translated by vector W. Let R be the vector from point N to point J. Let Z be point J translated by vector R. Let D be the line through point V parallel to segment PE. Line S is the angle bisector of angle UNZ. Let M be the line through point B perpendicular to line D. Point L is the reflection of point Z across line S. Point T is the reflection of point E across line M. What is the length of segment LT? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.88", "dataset": "MATH"}
{"messages": [{"content": "KP = 12. Let R be the perpendicular bisector of segment PK. Point B is on line R with |BP| = 12. Point D is the reflection of point K across point P. Let O be the midpoint of segment PB. Let E be the midpoint of segment OD. Point W is the reflection of point E across point P. What is the length of segment OW? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.12", "dataset": "MATH"}
{"messages": [{"content": "IW = 9. Point Y is the reflection of point W across point I. Point G is obtained by rotating point W by angle 2pi/3 about point I. Let C be the midpoint of segment GI. Let N be the rotation of point I by angle pi/12 around point G. Let P be the line through point W perpendicular to segment GY. Point T is the reflection of point Y across line P. Point K is the midpoint of segment TC. Find the distance between points K and N. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.83", "dataset": "MATH"}
{"messages": [{"content": "HX = 5. Let J be the line through points H and X. Let Z be the rotation of point X by angle pi/6 around point H. Let I be the reflection of point X across point H. Point E is the reflection of point I across point Z. Line N is the perpendicular bisector of segment HI. Let T be the midpoint of segment EH. Line S passes through point T parallel to line N. Point Q is the intersection of lines J and S. Find the distance between points H and Q. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.83", "dataset": "MATH"}
{"messages": [{"content": "EK = 9. Let X be the reflection of point K across point E. Let Y be the rotation of point K by angle pi/4 around point X. Let P be the reflection of point Y across point K. Let G be the reflection of point K across point Y. Point A is the midpoint of segment KE. Point C is the reflection of point A across point G. Point N is the reflection of point C across segment KE. What is the distance between points N and P? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44.0", "dataset": "MATH"}
{"messages": [{"content": "Let RA = 4. Point Z is obtained by rotating point R by angle 5pi/12 about point A. Line G passes through point Z perpendicular to segment RA. Line L passes through point A perpendicular to segment AZ. Let F be the reflection of point R across point A. Line D is the reflection of line G across point F. Let Y be the midpoint of segment RA. Point U is the reflection of point Y across line L. Point K is the reflection of point Z across line D. Point W is the reflection of point U across segment AZ. What is the length of segment KW? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.54", "dataset": "MATH"}
{"messages": [{"content": "DV = 2. Point Z is obtained by rotating point D by angle 7pi/12 about point V. Point Q is the reflection of point V across point D. Let R be the reflection of point Z across point Q. Let X be the reflection of point Q across point V. Let B be the perpendicular bisector of segment RV. Point G is the reflection of point Q across line B. Find the length of segment GX. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.91", "dataset": "MATH"}
{"messages": [{"content": "Let SG = 3. Let J be the midpoint of segment GS. Point V is obtained by rotating point S by angle 3pi/4 about point J. Let F be the angle bisector of angle GVS. Let I be the rotation of point S by angle 11pi/12 around point V. Point Y is the reflection of point I across segment VG. Line C is the reflection of line F across point I. Point O is the reflection of point I across line C. Point R is the reflection of point I across segment YV. Find the length of segment RO. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.77", "dataset": "MATH"}
{"messages": [{"content": "Let VL = 6. Let P be the reflection of point L across point V. Point R is the midpoint of segment LV. Line M is the angle bisector of angle RVP. Let Z be the reflection of point R across point P. Point J is the reflection of point Z across line M. Let N be the rotation of point P by angle pi/6 around point J. Let G be the midpoint of segment ZN. Let D be the reflection of line M through point J. Point B is the midpoint of segment LR. Point T is the reflection of point G across line D. Find the distance between points T and B. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64.81", "dataset": "MATH"}
{"messages": [{"content": "HD = 3. Point G is the reflection of point H across point D. Let S be the midpoint of segment GD. Let O be the perpendicular bisector of segment DH. Point C is the reflection of point G across line O. Point P is the midpoint of segment GS. What is the distance between points C and P? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.25", "dataset": "MATH"}
{"messages": [{"content": "Let FP = 2. Let I be the vector from point P to point F. Let G be the rotation of point F by angle pi around point P. Let E be the perpendicular bisector of segment GF. Let Z be the reflection of point F across point G. Let H be the perpendicular bisector of segment GP. Point M is the reflection of point Z across line H. Line W is the angle bisector of angle ZFM. Let K be the reflection of line E across line H. Point T lies on line E at distance 5 from point Z. Point C is the reflection of point Z across line W. Point J is the translation of point T by vector I. Let S be the reflection of point M across point T. Point Q is the reflection of point S across line K. Point V is the reflection of point P across segment JC. Let D be the line through point T perpendicular to segment VQ. Line U passes through point G perpendicular to line D. Point N is the reflection of point S across line U. What is the length of segment ZN? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.78", "dataset": "MATH"}
{"messages": [{"content": "NM = 10. Point T is the midpoint of segment MN. Point D is obtained by rotating point N by angle 5pi/6 about point M. Point F is the midpoint of segment DN. Point X is the reflection of point D across segment FT. Line K passes through points T and M. Let V be the line through point X perpendicular to line K. Point W is the reflection of point M across line V. What is the length of segment WX? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.18", "dataset": "MATH"}
{"messages": [{"content": "Let SN = 1. Let K be the rotation of point S by angle 5pi/12 around point N. Let C be the midpoint of segment SN. Let B be the rotation of point C by angle 5pi/6 around point N. Point M is the midpoint of segment CK. Let T be the rotation of point B by angle 7pi/12 around point C. Let R be the reflection of point T across point M. Point U is obtained by rotating point S by angle pi/3 about point N. Let D be the reflection of point M across point S. Point X is the reflection of point R across segment KD. Point V is the intersection of segments TU and DN. Find the distance between points X and V. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.68", "dataset": "MATH"}
{"messages": [{"content": "QA = 4. Point K is obtained by rotating point A by angle 2pi/3 about point Q. Let T be the perpendicular bisector of segment KQ. Line X passes through point Q parallel to line T. Let Z be the rotation of point Q by angle 5pi/12 around point K. Point H is the midpoint of segment KA. Let I be the line through point H parallel to line X. Let E be the line through point Z parallel to segment KA. Lines E and I intersect at point M. What is the distance between points M and K? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.83", "dataset": "MATH"}
{"messages": [{"content": "JV = 4. Let U be the reflection of point J across point V. Let Z be the rotation of point U by angle 3pi/4 around point J. Line G passes through points J and Z. Let F be the perpendicular bisector of segment JV. Let R be the reflection of line G across line F. Lines G and R intersect at point O. Point P is obtained by rotating point V by angle 5pi/6 about point J. Line E is the reflection of line F across point J. Line D passes through point Z parallel to line E. Line Q is the perpendicular bisector of segment OP. Line I passes through point V parallel to line Q. Line T is the reflection of line R across line I. Lines T and D intersect at point W. Line I and segment OW intersect at point K. Find the distance between points K and Z. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.76", "dataset": "MATH"}
{"messages": [{"content": "WK = 6. Line B passes through points K and W. Point I is obtained by rotating point K by angle 7pi/12 about point W. Point Y is the midpoint of segment WK. Let J be the perpendicular bisector of segment YK. Let C be the line through points I and K. Line H passes through point K parallel to line J. Point G is obtained by rotating point W by angle pi/2 about point K. Let P be the midpoint of segment IY. Let S be the midpoint of segment GI. Point R is the reflection of point Y across line H. Let V be the line through point W parallel to line C. Let F be the line through points K and P. Line E is the angle bisector of angle SRK. Let N be the reflection of line B across line E. Line T is the reflection of line N across line V. Lines F and T intersect at point Q. What is the distance between points Q and P? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.74", "dataset": "MATH"}
{"messages": [{"content": "Let NW = 7. Let V be the rotation of point N by angle pi/6 around point W. Line G is the angle bisector of angle VWN. Let U be the angle bisector of angle WVN. Let O be the reflection of point V across point W. Line I is the reflection of line U across line G. Point Q is the reflection of point W across line I. Let T be the reflection of point N across point W. Point L is the reflection of point O across segment VN. Point M is the reflection of point V across segment TN. Let B be the midpoint of segment ML. Find the length of segment BQ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.38", "dataset": "MATH"}
{"messages": [{"content": "TG = 12. Let V be the midpoint of segment GT. Let E be the rotation of point V by angle 7pi/12 around point T. Let O be the reflection of point T across point G. Point M is obtained by rotating point V by angle pi/3 about point T. Point Q is obtained by rotating point G by angle 2pi/3 about point E. Let R be the rotation of point Q by angle 7pi/12 around point V. Let I be the midpoint of segment VO. Point Y is the midpoint of segment EQ. Point H is the reflection of point I across point Y. Point F is the reflection of point H across segment GV. Point N is the reflection of point M across segment OR. Point X is the midpoint of segment NQ. Find the distance between points F and X. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36.64", "dataset": "MATH"}
{"messages": [{"content": "LO = 7. Let F be the line through points O and L. Point M is obtained by rotating point L by angle pi about point O. Line R passes through point M perpendicular to line F. Let S be the angle bisector of angle LOM. Let P be the reflection of point L across point M. Line K passes through point P parallel to line S. Point A is the reflection of point M across point P. Point H is the midpoint of segment PA. Let Y be the rotation of point L by angle 5pi/6 around point H. Point T is the reflection of point H across line R. Point W is the reflection of point T across line K. Let V be the midpoint of segment YW. Let X be the reflection of point M across point V. What is the length of segment YX? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49.0", "dataset": "MATH"}
{"messages": [{"content": "Let OW = 1. Point V is the midpoint of segment WO. Point P is obtained by rotating point W by angle pi about point O. Line I is the perpendicular bisector of segment WP. Line A is the reflection of line I across point V. Line Y is the reflection of line A across line I. Point U is on line A. Line M is the reflection of line Y across line A. Point R is the reflection of point U across line M. What is the length of segment UR? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "AC = 1. Let W be the rotation of point A by angle pi/6 around point C. Let V be the reflection of point W across point C. Point Z is the midpoint of segment AW. Line K passes through point W parallel to segment AC. Point D is the midpoint of segment VC. Let X be the reflection of point V across point W. Point F is the reflection of point Z across point X. Point Y is the reflection of point F across point A. Point U is the midpoint of segment YD. Point G is the intersection of line K and segment UF. What is the distance between points G and U? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.31", "dataset": "MATH"}
{"messages": [{"content": "XF = 7. Let D be the reflection of point F across point X. Let Z be the perpendicular bisector of segment XD. Line P passes through point D parallel to line Z. Let K be the line through point F perpendicular to segment XD. Point C lies on line K at distance 10 from point X. Point M lies on line P at distance 7 from point X. Point V is on segment XD. Line L is the perpendicular bisector of segment FC. Point J is on line L. Line N is the perpendicular bisector of segment MV. Let W be the reflection of point V across point J. Point H is the reflection of point F across line N. Let G be the midpoint of segment WH. What is the distance between points J and G? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.83", "dataset": "MATH"}
{"messages": [{"content": "Let JZ = 6. Point R is the midpoint of segment JZ. Line F is the perpendicular bisector of segment ZR. Point Y is the midpoint of segment RZ. Point O is obtained by rotating point Z by angle pi/6 about point R. Let D be the midpoint of segment JR. Let L be the rotation of point O by angle 7pi/12 around point Z. Let M be the reflection of point Y across point L. Let S be the reflection of line F through point D. Line C passes through point M parallel to segment RZ. Lines S and C intersect at point Q. What is the length of segment OQ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.73", "dataset": "MATH"}
{"messages": [{"content": "Let JH = 12. Point R is the reflection of point H across point J. Point K is the midpoint of segment RJ. Line A is the perpendicular bisector of segment KJ. Line D passes through point K parallel to line A. Point Q is the reflection of point H across line D. Point Z is the midpoint of segment QK. Find the length of segment KZ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.0", "dataset": "MATH"}
{"messages": [{"content": "Let VZ = 6. Let R be the reflection of point V across point Z. Point K is obtained by rotating point Z by angle pi about point R. Let W be the midpoint of segment ZR. Let Q be the midpoint of segment WK. Let F be the perpendicular bisector of segment QV. Point X is the reflection of point Z across line F. What is the distance between points V and X? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.5", "dataset": "MATH"}
{"messages": [{"content": "Let KC = 2. Line H passes through points K and C. Let G be the reflection of point C across point K. Let E be the angle bisector of angle CKG. Line X is the reflection of line E across point C. Let F be the reflection of point C across point G. Point L lies on line X at distance 5 from point C. Line J is the angle bisector of angle FGL. Let W be the reflection of line H across line J. Point R is the reflection of point C across line W. Point P is the reflection of point R across point F. Find the length of segment PK. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.42", "dataset": "MATH"}
{"messages": [{"content": "Let YO = 1. Line J passes through points Y and O. Let H be the reflection of point Y across point O. Let F be the rotation of point Y by angle pi/3 around point H. Point D is obtained by rotating point F by angle pi/3 about point H. Point W is the midpoint of segment DY. Point B is the reflection of point O across point F. Let G be the rotation of point Y by angle 5pi/6 around point W. Let C be the perpendicular bisector of segment GW. Let E be the reflection of line C across line J. Point U is the reflection of point H across line E. Let I be the midpoint of segment FB. Let R be the reflection of point U across point I. What is the length of segment RU? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.0", "dataset": "MATH"}
{"messages": [{"content": "YN = 10. Point Z is the reflection of point N across point Y. Let J be the perpendicular bisector of segment ZY. Let L be the reflection of line J through point Y. Point V is on line L with |VN| = 5. Line S is the perpendicular bisector of segment VZ. Point F is the reflection of point Y across line S. Point P is the reflection of point V across segment YF. Let G be the midpoint of segment YF. Let B be the reflection of point P across point Z. Let T be the midpoint of segment BG. Point E is the reflection of point T across segment YF. Point M is the midpoint of segment EG. What is the distance between points M and B? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.38", "dataset": "MATH"}
{"messages": [{"content": "MT = 1. Point X is the reflection of point T across point M. Let G be the rotation of point X by angle pi/2 around point M. Let L be the midpoint of segment TG. Let J be the reflection of point G across point T. Let C be the midpoint of segment XL. Point F is the reflection of point J across point C. What is the distance between points G and F? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.55", "dataset": "MATH"}
{"messages": [{"content": "Let WE = 10. Line Z is the perpendicular bisector of segment EW. Let L be the midpoint of segment EW. Let A be the rotation of point W by angle 5pi/6 around point E. Point F is obtained by rotating point W by angle pi/2 about point L. Line C passes through point A parallel to line Z. Point H is the reflection of point W across line C. Point T is the reflection of point A across point L. Let Y be the reflection of point T across point F. Find the distance between points H and Y. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.94", "dataset": "MATH"}
{"messages": [{"content": "Let HS = 7. Let HD = 10. Let V be the rotation of point H by angle 5pi/6 around point S. Point W lies on segment SH. Let J be the perpendicular bisector of segment SH. Point Q is the reflection of point H across segment DW. Line B passes through point Q perpendicular to segment SH. Point Z is the reflection of point V across line J. Let P be the line through point Z perpendicular to line B. Point M is the reflection of point W across line P. Find the distance between points W and M. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.0", "dataset": "MATH"}
{"messages": [{"content": "LG = 8. Let W be the reflection of point L across point G. Let E be the perpendicular bisector of segment LG. Point Q is obtained by rotating point L by angle pi/2 about point G. Point H is the reflection of point Q across line E. Point Y is the midpoint of segment WG. Point Z is the midpoint of segment LH. Let N be the rotation of point Y by angle pi/12 around point H. Let O be the midpoint of segment QZ. Point S is the reflection of point N across segment LH. Point U is the reflection of point O across segment LH. Let R be the midpoint of segment SQ. Find the length of segment UR. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.71", "dataset": "MATH"}
{"messages": [{"content": "RY = 3. Let K be the perpendicular bisector of segment YR. Point C is on segment YR. Let X be the angle bisector of angle RCY. Point I lies on line X. Let N be the rotation of point Y by angle pi around point C. Let Q be the line through point I perpendicular to line K. Point D is the midpoint of segment YR. Point L is the reflection of point R across line Q. Point G is the reflection of point N across point I. Point S is the reflection of point G across segment LD. Point J is the reflection of point S across segment CL. Find the distance between points J and L. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "UM = 5. Let T be the perpendicular bisector of segment UM. Let Q be the line through point M perpendicular to segment UM. Point G is the reflection of point M across point U. Line W is the reflection of line Q across line T. Let S be the reflection of line W across line Q. Point V lies on line S at distance 8 from point G. Point O is the reflection of point U across line Q. Line L is the reflection of line Q across line W. Point X is the reflection of point V across line W. Line Y passes through point U parallel to segment OX. Point C is the intersection of lines Y and L. Find the length of segment CO. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.13", "dataset": "MATH"}
{"messages": [{"content": "Let GI = 4. Point F is the midpoint of segment IG. Point D is obtained by rotating point I by angle 3pi/4 about point G. Line P passes through point I perpendicular to segment DG. Point C is the reflection of point G across line P. Line X passes through point D parallel to segment GF. Point O is the reflection of point C across line X. Let H be the angle bisector of angle FDC. Point A is the reflection of point O across segment DG. Point S is the reflection of point A across line H. Find the distance between points S and D. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.66", "dataset": "MATH"}
{"messages": [{"content": "Let ZQ = 12. Point K is obtained by rotating point Z by angle 2pi/3 about point Q. Let J be the reflection of point Q across point K. Point N is obtained by rotating point J by angle pi/2 about point Q. Let V be the midpoint of segment JN. Point F is the reflection of point V across segment JZ. Point O is the midpoint of segment ZV. Point E is the reflection of point O across segment JZ. Point M is the reflection of point E across segment JF. What is the distance between points F and M? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.37", "dataset": "MATH"}
{"messages": [{"content": "Let BJ = 7. Let V be the line through points B and J. Point D is obtained by rotating point J by angle 11pi/12 about point B. Point Y is the reflection of point J across point B. Let S be the perpendicular bisector of segment DB. Let R be the reflection of line S through point J. Let T be the midpoint of segment YD. Point P is the intersection of lines V and R. Point K is the reflection of point T across line V. Line H is the perpendicular bisector of segment PK. Point E is the reflection of point T across line H. Let C be the midpoint of segment PE. Point N is the reflection of point C across line H. Find the length of segment KN. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.91", "dataset": "MATH"}
{"messages": [{"content": "HV = 1. Let C be the rotation of point V by angle 5pi/6 around point H. Let F be the line through points C and H. Line M passes through point V parallel to line F. Let K be the midpoint of segment HV. Point P is the reflection of point K across point C. Let B be the rotation of point C by angle 5pi/6 around point V. Point S is the reflection of point P across line M. Line D is the angle bisector of angle VBC. Line Q passes through points S and P. Point R is the reflection of point H across point S. Point W is the reflection of point V across point S. Line A is the reflection of line Q across line D. Let O be the line through point W parallel to line D. Let L be the reflection of line O through point P. Point Y is the intersection of lines L and A. Point I is the reflection of point K across segment WR. Point J is the reflection of point Y across segment WR. Find the length of segment IJ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.21", "dataset": "MATH"}
{"messages": [{"content": "KF = 1. Point M is obtained by rotating point F by angle 2pi/3 about point K. Point R is the midpoint of segment FK. Let G be the reflection of point K across point F. Let Q be the reflection of point K across point M. Point J is the midpoint of segment FQ. Point X is the midpoint of segment RQ. Let N be the rotation of point G by angle 11pi/12 around point K. Line O is the perpendicular bisector of segment FK. Point Z is the reflection of point J across line O. Point S is the reflection of point Z across segment FQ. Let L be the midpoint of segment XN. What is the length of segment SL? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.48", "dataset": "MATH"}
{"messages": [{"content": "WX = 8. Point Y is obtained by rotating point W by angle pi/3 about point X. Point Q is the reflection of point Y across point W. Point P is the midpoint of segment YX. Point S is the reflection of point Y across segment XW. Let T be the reflection of point Q across point P. Let B be the line through points T and S. Point O is the reflection of point P across line B. Point I is the reflection of point W across line B. What is the length of segment IO? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.93", "dataset": "MATH"}
{"messages": [{"content": "Let QF = 4. Let V be the rotation of point Q by angle 11pi/12 around point F. Let J be the vector from point Q to point V. Point P is the translation of point F by vector J. Let T be the reflection of point P across point V. Let O be the rotation of point F by angle pi/12 around point T. Let D be the rotation of point Q by angle 5pi/6 around point P. Let E be point O translated by vector J. Let B be the perpendicular bisector of segment EQ. Point K is the reflection of point T across line B. Let W be the midpoint of segment OK. Let Z be the midpoint of segment WD. What is the distance between points K and Z? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.7", "dataset": "MATH"}
{"messages": [{"content": "VT = 2. Point C is the reflection of point T across point V. Let N be the angle bisector of angle TVC. Let Z be the rotation of point V by angle 7pi/12 around point C. Let F be the reflection of point V across point C. Let I be the vector from point F to point T. Let H be the line through points Z and F. Point X is the translation of point Z by vector I. Line S passes through point X perpendicular to line N. Line U passes through points X and F. Point P is the reflection of point V across line S. Let J be the reflection of line H across line S. Point E is the intersection of lines J and U. What is the distance between points P and E? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.57", "dataset": "MATH"}
{"messages": [{"content": "Let TG = 8. Let N be the perpendicular bisector of segment TG. Line L is the reflection of line N across point T. Point V lies on line L at distance 4 from point T. Point B is the midpoint of segment GT. Let J be the midpoint of segment VB. Point W is the reflection of point J across segment GT. Let M be the reflection of point W across point G. Find the length of segment WM. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.49", "dataset": "MATH"}
{"messages": [{"content": "Let ZX = 12. Let H be the midpoint of segment XZ. Point J is obtained by rotating point Z by angle pi/6 about point X. Let L be the perpendicular bisector of segment JH. Point T is the reflection of point Z across line L. Let B be the midpoint of segment TJ. Let F be the midpoint of segment ZJ. Point E is the reflection of point F across point T. What is the distance between points E and B? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.9", "dataset": "MATH"}
{"messages": [{"content": "Let OI = 7. Point G is obtained by rotating point I by angle pi/12 about point O. Let N be the midpoint of segment IO. Line H passes through point I perpendicular to segment OG. Line D is the reflection of line H across point G. Point R is the reflection of point N across line D. Let L be the midpoint of segment OR. Find the distance between points G and L. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.52", "dataset": "MATH"}
{"messages": [{"content": "GU = 12. Line X passes through point G perpendicular to segment UG. Line M passes through point U parallel to line X. Let O be the midpoint of segment GU. Let Y be the reflection of line M across line X. Point N is the reflection of point G across line Y. Point B is the midpoint of segment NO. What is the distance between points B and N? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.0", "dataset": "MATH"}
{"messages": [{"content": "BS = 11. Point X is obtained by rotating point B by angle 5pi/6 about point S. Line R passes through points X and B. Point L is the midpoint of segment SX. Point I is the reflection of point L across line R. What is the distance between points I and L? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.85", "dataset": "MATH"}
{"messages": [{"content": "Let IU = 6. Let O be the rotation of point U by angle 5pi/6 around point I. Let X be the reflection of point O across point U. Point T is on segment UI. Line D is the perpendicular bisector of segment TX. Point E is the reflection of point I across line D. Find the distance between points E and T. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.46", "dataset": "MATH"}
{"messages": [{"content": "Let WT = 2. Point H is obtained by rotating point T by angle pi/3 about point W. Point B is obtained by rotating point W by angle 5pi/12 about point H. Let Z be the reflection of point T across point B. Point P is the reflection of point H across point Z. Point S is the reflection of point P across segment BT. Find the distance between points H and S. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.57", "dataset": "MATH"}
{"messages": [{"content": "VC = 4. Point N is the reflection of point V across point C. Line Y is the angle bisector of angle CVN. Let W be the angle bisector of angle NCV. Let S be the rotation of point V by angle 5pi/6 around point C. Point H is the midpoint of segment SC. Let Z be the midpoint of segment HN. Point B is the reflection of point Z across line Y. Point U is the reflection of point N across segment CB. Line E is the perpendicular bisector of segment CB. Line J is the reflection of line E across point H. Let I be the line through point C parallel to line J. Let R be the reflection of line I across line W. Point K is the reflection of point U across line R. What is the length of segment KZ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.68", "dataset": "MATH"}
{"messages": [{"content": "Let JM = 8. Let X be the rotation of point J by angle pi/2 around point M. Let P be the midpoint of segment XM. Let O be the reflection of point J across point X. Point D is the reflection of point O across segment XM. Let Z be the midpoint of segment PJ. Point A is the midpoint of segment XD. What is the distance between points A and Z? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.0", "dataset": "MATH"}
{"messages": [{"content": "VB = 3. Let L be the reflection of point V across point B. Let M be the vector from point V to point B. Point Y is the reflection of point L across point V. Point D is the translation of point L by vector M. Line Q is the angle bisector of angle LBY. Point T is the reflection of point Y across line Q. Point S is on line Q with |SB| = 12. Line I is the angle bisector of angle SDB. Point O is the reflection of point L across point S. Point P is the reflection of point V across line I. Point K is the reflection of point O across point T. Point U is the midpoint of segment KP. What is the length of segment UD? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.68", "dataset": "MATH"}
{"messages": [{"content": "IK = 7. Let C be the vector from point K to point I. Let O be the rotation of point K by angle 11pi/12 around point I. Let F be the rotation of point I by angle 7pi/12 around point O. Let R be the reflection of point F across point K. Line L is the angle bisector of angle OKR. Point N is the translation of point O by vector C. Let Q be the line through points R and K. Let Y be the angle bisector of angle ORF. Let X be the reflection of point O across point N. Let E be the reflection of line Y across line L. Lines E and Q intersect at point A. What is the distance between points X and A? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32.24", "dataset": "MATH"}
{"messages": [{"content": "QP = 10. Let M be the vector from point Q to point P. Point N is the translation of point P by vector M. Let A be the line through points P and N. Point O is obtained by rotating point Q by angle pi/12 about point P. Point W is the midpoint of segment OQ. Point V is the reflection of point P across point O. Line U is the reflection of line A across point V. Let D be the line through points O and N. Point R is the midpoint of segment QW. Point Y is the reflection of point W across line D. Point Z is the reflection of point Y across line U. Let B be the midpoint of segment ZR. What is the length of segment BZ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.09", "dataset": "MATH"}
{"messages": [{"content": "OE = 6. Point K is the midpoint of segment EO. Point Q is the reflection of point O across point E. Point X is the midpoint of segment KO. Let R be the rotation of point E by angle 5pi/6 around point X. Let D be the rotation of point O by angle 5pi/6 around point Q. Let P be the reflection of point O across point Q. Let J be the midpoint of segment PR. Line L passes through point X perpendicular to segment ED. Let V be the line through point Q parallel to line L. Point H is the reflection of point J across line V. What is the distance between points J and H? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.02", "dataset": "MATH"}
{"messages": [{"content": "Let HT = 10. Let M be the perpendicular bisector of segment TH. Point X is on line M with |XH| = 8. Point P is the midpoint of segment XT. Line R passes through point T perpendicular to segment HX. Let Y be the reflection of point P across point X. Point U is the reflection of point Y across line R. What is the distance between points U and H? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.33", "dataset": "MATH"}
{"messages": [{"content": "WT = 11. Let R be the midpoint of segment WT. Point S is the midpoint of segment RT. Point Z is the midpoint of segment RS. Find the distance between points Z and R. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.38", "dataset": "MATH"}
{"messages": [{"content": "VY = 5. Let Q be the vector from point Y to point V. Let L be the midpoint of segment VY. Line N is the perpendicular bisector of segment VY. Point J lies on line N at distance 3 from point Y. Point A is the translation of point J by vector Q. Point S is the translation of point L by vector Q. Point C is the midpoint of segment LA. Let W be the line through point C parallel to segment AJ. Point M is on segment AJ. Let I be the reflection of line W through point M. Point P is the reflection of point A across line I. Find the distance between points S and P. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.0", "dataset": "MATH"}
{"messages": [{"content": "Let EV = 7. Let P be the vector from point V to point E. Let Z be the reflection of point V across point E. Point H is obtained by rotating point V by angle pi/2 about point E. Let L be the rotation of point Z by angle 11pi/12 around point E. Let I be point Z translated by vector P. Line Y is the perpendicular bisector of segment ZH. Line X is the reflection of line Y across point H. Let O be the rotation of point I by angle pi around point E. Let T be the reflection of point L across point I. Let R be the reflection of point T across point O. Let S be the rotation of point R by angle pi/6 around point T. Let M be the reflection of line X through point S. Point N is the reflection of point O across line M. Point Q is the reflection of point T across segment NI. Find the length of segment QL. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29.15", "dataset": "MATH"}
{"messages": [{"content": "Let ZA = 1. Let F be the perpendicular bisector of segment ZA. Let O be the midpoint of segment ZA. Point K is on line F with |KO| = 2. Point R is the midpoint of segment ZO. Point W is the midpoint of segment RA. Line G is the perpendicular bisector of segment KA. Let D be the line through point O parallel to line G. Point X is the intersection of line D and segment KA. Find the length of segment XW. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
{"messages": [{"content": "TP = 4. Point B is the midpoint of segment TP. Let V be the reflection of point B across point P. Line M is the perpendicular bisector of segment TB. Point E is obtained by rotating point V by angle pi/2 about point T. Point U is obtained by rotating point E by angle 11pi/12 about point P. Let A be the line through point E perpendicular to segment UT. Point N is the reflection of point U across line A. Point Y is the reflection of point N across line M. Point W is the reflection of point Y across segment UT. What is the distance between points Y and W? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39.05", "dataset": "MATH"}
{"messages": [{"content": "Let CO = 7. Let J be the rotation of point O by angle pi/2 around point C. Let U be the midpoint of segment CJ. Let Q be the rotation of point U by angle pi/2 around point O. Point H is obtained by rotating point Q by angle pi/4 about point O. Let D be the reflection of point U across point O. Point V is the reflection of point H across point D. Let B be the midpoint of segment CD. What is the length of segment VB? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.73", "dataset": "MATH"}
{"messages": [{"content": "HR = 3. Point G is the reflection of point R across point H. Line C passes through points R and G. Let P be the rotation of point H by angle 3pi/4 around point R. Let S be the rotation of point R by angle pi/3 around point H. Let N be the reflection of point G across point P. Let D be the line through point S parallel to line C. Let E be the midpoint of segment HN. Point W is the reflection of point P across line D. Let K be the midpoint of segment WE. Point I is the midpoint of segment KP. What is the distance between points I and N? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.95", "dataset": "MATH"}
{"messages": [{"content": "Let BX = 5. Point Z is obtained by rotating point B by angle pi/12 about point X. Let D be the reflection of point B across point Z. Line Q is the perpendicular bisector of segment BX. Line O passes through point D parallel to line Q. Let V be the line through point B perpendicular to segment DX. Let K be the reflection of line V through point D. Point T is the intersection of lines K and O. Let F be the midpoint of segment DX. Point W is the midpoint of segment TF. Find the length of segment WZ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.11", "dataset": "MATH"}
{"messages": [{"content": "VG = 3. Point E is obtained by rotating point G by angle 11pi/12 about point V. Let W be the midpoint of segment GV. Line Z is the angle bisector of angle VWE. Let S be the midpoint of segment EV. Point R is the reflection of point G across segment VE. Point P is the reflection of point S across line Z. Let N be the midpoint of segment PR. What is the distance between points R and N? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.19", "dataset": "MATH"}
{"messages": [{"content": "XO = 9. Point Y is the reflection of point O across point X. Point M is the midpoint of segment XY. Line S is the angle bisector of angle YMX. Let N be the rotation of point O by angle pi/4 around point M. Let U be the line through points Y and M. Line W is the reflection of line S across point N. Let Z be the reflection of point X across point Y. Line L is the angle bisector of angle NMX. Point B is the midpoint of segment YN. Point P is the intersection of lines U and W. Point T is the midpoint of segment PN. Let G be the reflection of line L through point N. Point R is the reflection of point T across line G. Point K is the reflection of point Z across point R. What is the length of segment BK? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51.88", "dataset": "MATH"}
{"messages": [{"content": "Let SJ = 12. Point U is obtained by rotating point S by angle pi/2 about point J. Point W is the reflection of point S across point J. Let A be the perpendicular bisector of segment UJ. Point C is the midpoint of segment JW. Let Y be the midpoint of segment UJ. Let V be the reflection of point U across point W. Line B passes through point V perpendicular to line A. Point N is the reflection of point J across line B. Point K is the reflection of point Y across point N. Find the length of segment CK. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90.2", "dataset": "MATH"}
{"messages": [{"content": "Let QR = 11. Let X be the reflection of point R across point Q. Let C be the midpoint of segment QR. Line I is the perpendicular bisector of segment QC. Let O be the rotation of point R by angle 7pi/12 around point Q. Let A be the reflection of line I through point Q. Let H be the reflection of point Q across point R. Point Z is the midpoint of segment XQ. Let S be the midpoint of segment XO. Point D is the reflection of point Z across point S. Point F is the reflection of point D across line A. Point M is the reflection of point F across segment XR. Find the length of segment HM. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.9", "dataset": "MATH"}
{"messages": [{"content": "JB = 10. Point H is the midpoint of segment BJ. Point N is the midpoint of segment JH. Point S is obtained by rotating point N by angle pi/4 about point B. Let L be the perpendicular bisector of segment HS. Point I is the midpoint of segment BH. Point Z is the reflection of point N across line L. What is the length of segment ZI? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.29", "dataset": "MATH"}
{"messages": [{"content": "Let OI = 10. Line K is the perpendicular bisector of segment OI. Line G passes through point I parallel to line K. Let C be the midpoint of segment OI. Line V is the reflection of line K across line G. Let H be the line through points C and I. Point U is obtained by rotating point O by angle 3pi/4 about point I. Point M is obtained by rotating point C by angle pi/4 about point I. Let S be the reflection of point C across point I. Let F be the perpendicular bisector of segment IU. Let R be the reflection of line F across line V. Point L is the intersection of lines R and H. Point X is the reflection of point C across point S. Lines R and G intersect at point J. Point Z is the reflection of point L across point U. Point D is the midpoint of segment MJ. Point E is the midpoint of segment DX. What is the length of segment EZ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.73", "dataset": "MATH"}
{"messages": [{"content": "QT = 10. Let Y be the reflection of point T across point Q. Point F is the midpoint of segment YQ. Point D is the midpoint of segment QT. Let E be the rotation of point Q by angle pi/6 around point F. Let M be the perpendicular bisector of segment YE. Line U is the reflection of line M across point Y. Let G be the rotation of point E by angle pi/12 around point D. Point S is the reflection of point T across point Y. Let A be the midpoint of segment SY. Let V be the reflection of line M across line U. Point B is the reflection of point G across point E. Point L is the midpoint of segment FB. Let I be the line through point B parallel to line M. Let P be the angle bisector of angle BYA. Let R be the line through point L perpendicular to line I. Let Z be the rotation of point A by angle pi/3 around point B. Line W is the reflection of line R across line P. Lines W and V intersect at point O. Line X is the reflection of line I across point S. Let H be the midpoint of segment ZL. Point C is the reflection of point O across line X. Point K is the midpoint of segment CH. What is the distance between points K and Z? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41.47", "dataset": "MATH"}
{"messages": [{"content": "Let IJ = 12. Point E is the midpoint of segment IJ. Let A be the rotation of point J by angle 7pi/12 around point E. Z is placed 12 units away from J. Let H be the midpoint of segment AI. Point B is the midpoint of segment ZE. Point K is the reflection of point B across point A. Let D be the perpendicular bisector of segment BK. Point L is the reflection of point H across line D. What is the distance between points L and A? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.65", "dataset": "MATH"}
{"messages": [{"content": "SD = 7. Let X be the reflection of point D across point S. Point Z is the reflection of point X across point D. Let G be the reflection of point D across point X. Let V be the midpoint of segment ZD. Line M passes through point G perpendicular to segment XG. Point P is the midpoint of segment VG. Point K is the midpoint of segment DP. Point H is the reflection of point X across line M. Point O is the reflection of point H across point Z. Let I be the reflection of point K across point D. What is the distance between points O and I? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64.75", "dataset": "MATH"}
{"messages": [{"content": "WL = 1. Let D be the line through points L and W. Point S is the midpoint of segment WL. Point U is obtained by rotating point W by angle 7pi/12 about point S. Let H be the reflection of line D through point U. Let O be the reflection of line H across line D. Point M is on line O with |MS| = 12. Line Z is the perpendicular bisector of segment SU. Let C be the reflection of line Z through point S. Line X passes through point M parallel to line C. Let Y be the line through point S perpendicular to line X. Point R is the reflection of point L across line Y. Find the distance between points R and W. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.26", "dataset": "MATH"}
{"messages": [{"content": "Let SC = 9. Line P is the perpendicular bisector of segment CS. Let Y be the rotation of point C by angle pi/4 around point S. Let D be the rotation of point C by angle 7pi/12 around point Y. Point E is the reflection of point D across line P. Line U passes through points D and S. Let G be the reflection of point Y across point E. Point X is the midpoint of segment EC. Line I is the reflection of line U across point Y. Point K is the reflection of point X across line I. Let A be the line through points D and Y. Let T be the line through point K perpendicular to line A. Point W is the midpoint of segment GX. Point V is the reflection of point W across line T. Let M be the reflection of point V across point X. What is the distance between points M and W? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.71", "dataset": "MATH"}
{"messages": [{"content": "VN = 1. Line U is the perpendicular bisector of segment NV. Line Y is the reflection of line U across point V. Line L passes through point N parallel to line U. Point R is the reflection of point V across line L. Point X is obtained by rotating point V by angle 3pi/4 about point N. Let D be the line through points N and X. Line H is the reflection of line U across line D. Lines H and Y intersect at point O. Let E be the midpoint of segment OR. Point J is the midpoint of segment EN. Point P is the midpoint of segment EJ. What is the distance between points P and J? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.09", "dataset": "MATH"}
{"messages": [{"content": "Let RZ = 2. Point L is obtained by rotating point R by angle pi/2 about point Z. Point X is the reflection of point L across point Z. Point N is obtained by rotating point Z by angle 7pi/12 about point R. Let S be the rotation of point X by angle pi/6 around point L. Point E is the reflection of point L across point S. Line K passes through point R parallel to segment XN. Point J is the reflection of point E across line K. Let G be the reflection of point X across point J. What is the distance between points G and S? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.58", "dataset": "MATH"}
{"messages": [{"content": "MF = 10. Point X is the midpoint of segment FM. Let B be the rotation of point M by angle 3pi/4 around point X. Let E be the reflection of point M across point B. Point R is the midpoint of segment XB. Point G is the reflection of point B across point F. Point P is the reflection of point G across point R. Find the distance between points E and P. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.0", "dataset": "MATH"}
{"messages": [{"content": "Let GP = 2. Let O be the perpendicular bisector of segment PG. Point K is the midpoint of segment GP. Line U passes through point P parallel to line O. Point Z is on line U with |ZK| = 9. Line S is the angle bisector of angle PGZ. Line W is the reflection of line U across line S. Point N is the reflection of point Z across line W. Let E be the reflection of point G across point Z. Point I is the reflection of point E across segment NP. Find the length of segment NI. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.66", "dataset": "MATH"}
{"messages": [{"content": "Let OX = 7. Let Y be the midpoint of segment OX. Let B be the rotation of point O by angle 7pi/12 around point Y. Point R is the reflection of point B across point X. Let V be the reflection of point B across point Y. Line C is the angle bisector of angle VRX. Point W is the reflection of point O across point V. Point M is the reflection of point Y across line C. Point H is the reflection of point V across point M. Let F be the midpoint of segment WV. What is the length of segment FH? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.24", "dataset": "MATH"}
{"messages": [{"content": "JR = 4. Point S is the midpoint of segment JR. Point D is obtained by rotating point R by angle pi/12 about point S. Point E is the midpoint of segment DR. Line F is the angle bisector of angle SEJ. Let K be the vector from point J to point E. Let G be point D translated by vector K. Point N is obtained by rotating point R by angle 5pi/6 about point G. Let W be the midpoint of segment RN. Point Z is the reflection of point W across line F. Point B is the reflection of point W across point N. Point H is the midpoint of segment BN. Point Y is the midpoint of segment BZ. What is the distance between points H and Y? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.24", "dataset": "MATH"}
{"messages": [{"content": "Let AK = 5. Let W be the vector from point A to point K. Let J be point K translated by vector W. Point F is the midpoint of segment JK. Point M is the translation of point J by vector W. Line I passes through point K perpendicular to segment AK. Let O be the reflection of line I through point F. Line P is the perpendicular bisector of segment AK. Point D is on line I with |DM| = 6. Let G be the reflection of line O across line P. Line U passes through point J parallel to segment MD. Point E is the intersection of lines U and G. What is the distance between points E and J? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.49", "dataset": "MATH"}
{"messages": [{"content": "Let NE = 1. Let A be the perpendicular bisector of segment NE. Point W is the reflection of point E across point N. Point P is obtained by rotating point E by angle 2pi/3 about point W. Point B is obtained by rotating point W by angle 11pi/12 about point N. Let O be the midpoint of segment PN. Point K is the midpoint of segment WO. Point Y is the midpoint of segment PB. Point D is the reflection of point K across line A. Let Z be the reflection of point D across point P. What is the length of segment YZ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.94", "dataset": "MATH"}
{"messages": [{"content": "YS = 1. Let N be the midpoint of segment YS. Let O be the rotation of point S by angle 5pi/6 around point Y. Line U passes through points O and N. Point P is obtained by rotating point Y by angle pi/4 about point O. Let W be the rotation of point P by angle 5pi/6 around point S. Let R be the midpoint of segment OY. Point L is the midpoint of segment WO. Point C is the reflection of point R across line U. Find the distance between points L and C. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.96", "dataset": "MATH"}
{"messages": [{"content": "Let SR = 9. Let E be the vector from point R to point S. Let SI = 9. Let D be the line through points I and R. Let U be the midpoint of segment IS. Point K is obtained by rotating point U by angle 2pi/3 about point S. Let Z be point S translated by vector E. Point B is the reflection of point Z across line D. Point N is the reflection of point I across segment BU. Let H be the midpoint of segment IK. Point O is the reflection of point H across segment BU. What is the distance between points N and O? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.95", "dataset": "MATH"}
{"messages": [{"content": "Let TI = 6. Let E be the line through points I and T. Let A be the line through point T perpendicular to line E. Line R passes through point I parallel to line A. Let X be the perpendicular bisector of segment TI. Point L is on line R with |LT| = 11. Point D is the reflection of point L across line X. Point Z is the midpoint of segment LD. Point W is the midpoint of segment ZI. Let V be the reflection of point W across point Z. What is the distance between points V and T? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.57", "dataset": "MATH"}
{"messages": [{"content": "AD = 9. Let H be the rotation of point D by angle 5pi/6 around point A. Let B be the perpendicular bisector of segment HA. Line W is the reflection of line B across point D. Let K be the reflection of point A across point D. Point I is the reflection of point D across line W. Let U be the midpoint of segment KH. Find the measure of angle KIU, in radians. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.26", "dataset": "MATH"}
{"messages": [{"content": "Let PK = 9. Let M be the rotation of point K by angle 11pi/12 around point P. Let J be the vector from point K to point P. Let N be the perpendicular bisector of segment MP. Point B is the reflection of point M across point K. Let G be point M translated by vector J. Line D is the perpendicular bisector of segment PB. Line F is the reflection of line D across line N. Point Z is the reflection of point B across line F. Point E is the midpoint of segment ZG. What is the length of segment PE? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43.4", "dataset": "MATH"}
{"messages": [{"content": "Let ST = 3. Let A be the perpendicular bisector of segment TS. Point F lies on line A. Point L is the reflection of point S across point T. Point C is the reflection of point S across segment FL. What is the length of segment LC? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.0", "dataset": "MATH"}
{"messages": [{"content": "Let LA = 11. Point N is the reflection of point L across point A. Let F be the reflection of point A across point L. Let V be the perpendicular bisector of segment AF. Line J is the reflection of line V across point N. Point K is the reflection of point N across line J. What is the distance between points F and K? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77.0", "dataset": "MATH"}
{"messages": [{"content": "Let MA = 11. Let Z be the rotation of point M by angle pi/12 around point A. Let J be the reflection of point A across point Z. Let V be the midpoint of segment ZM. Let X be the perpendicular bisector of segment MV. Point F lies on line X at distance 3 from point M. Let W be the midpoint of segment FV. Point U is the reflection of point F across segment JZ. Point N is the reflection of point W across segment JZ. What is the length of segment UN? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.54", "dataset": "MATH"}
{"messages": [{"content": "DJ = 11. Let E be the reflection of point J across point D. Let V be the vector from point J to point E. Line G passes through point E perpendicular to segment DJ. Let S be the midpoint of segment DJ. Let X be the reflection of line G through point S. Point Y is on line G with |YE| = 1. Point F is the translation of point S by vector V. Point W is the translation of point D by vector V. Line Q is the perpendicular bisector of segment FY. Point N is the reflection of point W across point S. Line O is the reflection of line X across point Y. Let Z be the line through point W parallel to line G. Line U is the reflection of line Z across line O. Let C be the line through point D perpendicular to line Q. Point K is the reflection of point Y across line U. Point P is the midpoint of segment SN. Point L is the reflection of point P across line C. Find the distance between points K and L. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "139.14", "dataset": "MATH"}
{"messages": [{"content": "GF = 8. Point Z is obtained by rotating point G by angle pi/12 about point F. Let I be the perpendicular bisector of segment GF. Line M passes through point Z perpendicular to line I. Let D be the midpoint of segment GZ. Point U is the reflection of point F across line M. Point T is the reflection of point F across segment ZG. Let J be the midpoint of segment UD. What is the length of segment TJ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.81", "dataset": "MATH"}
{"messages": [{"content": "Let KY = 7. Point M is the reflection of point Y across point K. Let B be the midpoint of segment KM. Let E be the reflection of point K across point M. Let P be the rotation of point K by angle pi/2 around point Y. Line F is the perpendicular bisector of segment KP. Point H is obtained by rotating point P by angle pi/3 about point K. Let J be the midpoint of segment MB. Point U is the reflection of point H across segment KE. Line V passes through points J and U. Let G be the reflection of line F across line V. Lines G and V intersect at point W. Find the distance between points K and W. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.5", "dataset": "MATH"}
{"messages": [{"content": "Let YS = 5. Point J is obtained by rotating point Y by angle pi/12 about point S. Let Z be the reflection of point J across point S. Let F be the perpendicular bisector of segment JS. Point X is the reflection of point J across point Y. Let E be the perpendicular bisector of segment SY. Let I be the rotation of point S by angle pi/2 around point Z. Let O be the rotation of point J by angle pi/4 around point S. Point M is obtained by rotating point Z by angle pi/6 about point I. Point H is the midpoint of segment SX. Point A is obtained by rotating point M by angle pi about point J. Line G is the reflection of line F across line E. Point L is the intersection of line G and segment OA. Point D is the reflection of point M across segment SL. Find the length of segment HD. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.89", "dataset": "MATH"}
{"messages": [{"content": "JU = 12. Point M is the midpoint of segment UJ. Let Y be the line through point U perpendicular to segment UJ. Point E is the reflection of point M across line Y. What is the distance between points M and E? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.0", "dataset": "MATH"}
{"messages": [{"content": "Let GH = 10. Line M is the perpendicular bisector of segment HG. Let D be the rotation of point G by angle pi/2 around point H. Point S is obtained by rotating point H by angle pi/2 about point G. Point C is obtained by rotating point S by angle 3pi/4 about point H. Let N be the line through point C parallel to line M. Line Z is the reflection of line N across line M. Let O be the rotation of point H by angle 11pi/12 around point G. Line W is the reflection of line N across point S. Point P is the reflection of point O across point G. Point Q is the reflection of point G across point P. Line T is the reflection of line Z across line W. Point K is the reflection of point S across line T. Point Y is the reflection of point Q across point K. Find the length of segment YD. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114.84", "dataset": "MATH"}
{"messages": [{"content": "Let PW = 12. Point Q is obtained by rotating point P by angle 5pi/12 about point W. Let K be the midpoint of segment QP. Let B be the rotation of point W by angle 2pi/3 around point P. Line O is the perpendicular bisector of segment KB. Line E passes through point K parallel to line O. Line U passes through point B perpendicular to line E. Point X is the reflection of point P across line U. Let D be the reflection of point X across point P. Point C is the reflection of point K across point D. What is the length of segment KC? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.99", "dataset": "MATH"}
{"messages": [{"content": "LZ = 2. Let D be the vector from point Z to point L. Point F is the reflection of point Z across point L. Point H is the translation of point F by vector D. Point K is obtained by rotating point Z by angle pi/12 about point H. Let T be the midpoint of segment FK. Point A is the reflection of point H across point T. Point W is the reflection of point F across segment HK. Point Q is the reflection of point Z across point W. Find the length of segment QA. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.34", "dataset": "MATH"}
{"messages": [{"content": "AH = 2. Point E is the reflection of point A across point H. Let R be the midpoint of segment HA. Let O be the rotation of point E by angle 3pi/4 around point R. Let D be the angle bisector of angle EOH. Let S be the reflection of line D through point R. Line I passes through points E and H. Lines I and S intersect at point U. Line F is the reflection of line S across point A. Point Z is the reflection of point U across line F. Point L is the midpoint of segment AZ. Let M be the midpoint of segment ZR. Find the distance between points M and L. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "HT = 8. Let K be the rotation of point T by angle pi/4 around point H. Let E be the line through points H and K. Point D is the reflection of point T across point K. Point M is the reflection of point D across line E. Line F is the angle bisector of angle THM. Point N is the reflection of point M across line F. Line W is the perpendicular bisector of segment ND. Point P is the reflection of point H across point T. Point O is the reflection of point P across line W. Point X is the midpoint of segment OD. What is the length of segment OX? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.11", "dataset": "MATH"}
{"messages": [{"content": "Let EW = 5. Let L be the midpoint of segment WE. Let S be the rotation of point W by angle 7pi/12 around point L. Point P is the reflection of point L across point W. Point N is the midpoint of segment EP. Point T is the midpoint of segment NS. Find the distance between points T and S. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.54", "dataset": "MATH"}
{"messages": [{"content": "TW = 10. Line H passes through points W and T. Point K is obtained by rotating point W by angle 3pi/4 about point T. Let O be the angle bisector of angle TKW. Point J is the midpoint of segment WK. Point Q is the reflection of point J across line O. Line L is the reflection of line H across line O. Let P be the rotation of point T by angle 11pi/12 around point K. Let C be the reflection of line H across line L. Let E be the line through points K and T. Let A be the rotation of point Q by angle pi/6 around point K. Let F be the reflection of line O across line E. Point D is the reflection of point A across segment PW. Point V is the intersection of lines C and F. What is the length of segment VD? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.12", "dataset": "MATH"}
{"messages": [{"content": "KM = 12. L is constructed so that ML = 9. Let N be the perpendicular bisector of segment LM. Point D is the reflection of point M across point L. Point T lies on line N. Point X is the reflection of point D across point T. Point Z is the reflection of point X across line N. Find the distance between points Z and X. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.0", "dataset": "MATH"}
{"messages": [{"content": "IX = 4. Let T be the reflection of point I across point X. Point F is the reflection of point I across point T. Point M is the reflection of point I across point F. Let O be the midpoint of segment XT. Let G be the midpoint of segment XM. Point B is the midpoint of segment GT. Find the distance between points B and O. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.0", "dataset": "MATH"}
{"messages": [{"content": "Let YX = 10. Let O be the reflection of point Y across point X. Let H be the rotation of point O by angle 5pi/12 around point X. Point B is the midpoint of segment YH. Let K be the midpoint of segment XY. Let C be the midpoint of segment KB. What is the length of segment KC? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Let FV = 8. Let Q be the rotation of point V by angle 5pi/6 around point F. Point N is the reflection of point V across point F. Point I is obtained by rotating point F by angle 3pi/4 about point V. Point T is the reflection of point F across segment VI. Let W be the midpoint of segment TN. Let O be the midpoint of segment FQ. Let R be the midpoint of segment OW. Let Z be the midpoint of segment VQ. Point A is the midpoint of segment ZR. Find the distance between points W and A. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.61", "dataset": "MATH"}
{"messages": [{"content": "Let RU = 6. Point I is obtained by rotating point R by angle pi/6 about point U. Point Q lies on segment IU. Point B is the reflection of point R across point Q. Line M is the perpendicular bisector of segment UR. Line T passes through point Q perpendicular to line M. Point H is the reflection of point I across line T. Point P is the reflection of point H across point B. Point W is the reflection of point U across point P. Point N is the midpoint of segment WI. What is the length of segment PN? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "JF = 5. Let M be the rotation of point J by angle pi/12 around point F. Point D is obtained by rotating point M by angle pi/12 about point F. Let H be the reflection of point F across point D. Point N is obtained by rotating point H by angle 11pi/12 about point F. Let L be the reflection of point D across point F. Point P is the reflection of point L across segment JF. Point G is the midpoint of segment PN. Point C is the midpoint of segment GH. What is the length of segment HC? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.22", "dataset": "MATH"}
{"messages": [{"content": "Let CU = 2. Let S be the perpendicular bisector of segment CU. Let F be the line through point C parallel to line S. Let L be the midpoint of segment UC. Point A is obtained by rotating point U by angle pi/6 about point L. Point E is obtained by rotating point A by angle 7pi/12 about point U. Point Z is obtained by rotating point A by angle pi/2 about point L. Point W is the reflection of point A across line F. Let H be the reflection of point A across point Z. Point K is the reflection of point H across segment UA. Let J be the reflection of point L across point E. Let T be the midpoint of segment JW. What is the length of segment TK? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.51", "dataset": "MATH"}
{"messages": [{"content": "Let FY = 7. Let Q be the vector from point F to point Y. Point I is the midpoint of segment YF. Point A is the translation of point Y by vector Q. Let C be the midpoint of segment IF. Point K is the reflection of point C across point A. Point P is obtained by rotating point F by angle pi/12 about point A. Let V be the rotation of point Y by angle pi/12 around point P. Let U be the midpoint of segment VK. Point X is the midpoint of segment UA. Let N be the midpoint of segment IA. Let H be the midpoint of segment CN. Find the length of segment HX. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.78", "dataset": "MATH"}
{"messages": [{"content": "Let MG = 9. Let Q be the perpendicular bisector of segment GM. Point I is the midpoint of segment GM. Line N passes through point M parallel to line Q. Point E is on line N with |EM| = 2. Line D is the angle bisector of angle EIM. Point Y is the reflection of point M across line D. Point C is the reflection of point E across point Y. Let J be the perpendicular bisector of segment IG. Let R be the reflection of line J across line N. Line T is the reflection of line R across line D. Let P be the reflection of point Y across point E. Point F is the midpoint of segment CM. Point X is the reflection of point F across segment CE. Line O passes through point P parallel to segment EG. Line V passes through point X parallel to line T. Let S be the midpoint of segment EG. Let U be the perpendicular bisector of segment EG. Line B passes through point I parallel to line U. Line H is the reflection of line O across line V. Lines B and H intersect at point A. What is the distance between points A and S? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "IY = 5. Point M is the midpoint of segment IY. Point H is the reflection of point M across point Y. Point S is the reflection of point Y across point H. Let J be the reflection of point M across point I. What is the distance between points J and S? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.5", "dataset": "MATH"}
{"messages": [{"content": "Let BW = 9. Point N is the reflection of point W across point B. Let H be the rotation of point W by angle 11pi/12 around point B. Point I is obtained by rotating point W by angle pi/3 about point N. Point J is the midpoint of segment IN. Point U is the midpoint of segment HB. Point L is the reflection of point I across segment JU. What is the length of segment LN? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.38", "dataset": "MATH"}
{"messages": [{"content": "Let BI = 11. Point V is obtained by rotating point B by angle 5pi/6 about point I. Let L be the angle bisector of angle IVB. Point P is the reflection of point V across point B. Let W be the midpoint of segment BP. Line Q passes through point W perpendicular to line L. Point K is the reflection of point V across line Q. Find the distance between points P and K. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.79", "dataset": "MATH"}
{"messages": [{"content": "WJ = 4. Line M is the perpendicular bisector of segment JW. Let P be the rotation of point W by angle 7pi/12 around point J. Line E is the reflection of line M across point P. Let K be the line through points P and W. Let U be the reflection of line M across line K. Point O is the intersection of lines U and K. Lines E and U intersect at point I. Line X is the angle bisector of angle JOP. Let G be the midpoint of segment JP. Let L be the midpoint of segment IP. Let Q be the midpoint of segment GP. Point F is the reflection of point Q across line X. Point B is the reflection of point G across point L. Point T is the midpoint of segment BF. Find the distance between points T and L. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.89", "dataset": "MATH"}
{"messages": [{"content": "ZR = 1. Let K be the rotation of point R by angle 11pi/12 around point Z. Line T passes through points Z and K. Point Y is the midpoint of segment KR. Let N be the line through point Z perpendicular to segment ZR. Line F is the reflection of line N across line T. Let H be the reflection of point Y across point Z. Point O is the reflection of point H across line F. Point X is the reflection of point H across segment ZR. What is the length of segment XO? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
{"messages": [{"content": "GU = 10. Let Q be the line through points G and U. Let X be the rotation of point U by angle pi/4 around point G. Point A is on line Q. Let I be the line through point U perpendicular to line Q. Let Z be the rotation of point A by angle 5pi/12 around point U. Point R is the reflection of point X across line I. Let D be the midpoint of segment RU. Let Y be the midpoint of segment RD. Let F be the reflection of point D across point U. Let T be the midpoint of segment ZY. Let N be the reflection of point T across point F. Point C is the reflection of point T across point R. What is the distance between points N and C? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.96", "dataset": "MATH"}
{"messages": [{"content": "Let KI = 1. Line A is the perpendicular bisector of segment KI. Let E be the reflection of point K across point I. Point T is obtained by rotating point K by angle 3pi/4 about point E. Point X is the reflection of point T across segment KI. Point L is the midpoint of segment KX. Point O is the reflection of point L across line A. Point W is obtained by rotating point K by angle 5pi/6 about point X. Point B is the reflection of point L across segment EX. Let M be the line through points B and L. Point Q is the intersection of line M and segment WE. Point R is the midpoint of segment QO. What is the length of segment RE? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.24", "dataset": "MATH"}
{"messages": [{"content": "Let CX = 9. Point I is obtained by rotating point X by angle pi about point C. Let Y be the rotation of point I by angle pi/3 around point X. Point E is the midpoint of segment XC. Point B is the reflection of point X across point Y. Let A be the reflection of point E across point X. Line P is the perpendicular bisector of segment IC. Let J be the reflection of line P through point B. Line S passes through points A and X. Let Q be the reflection of point A across point B. Point H is the intersection of lines J and S. What is the length of segment HQ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64.9", "dataset": "MATH"}
{"messages": [{"content": "HV = 7. Point F is the midpoint of segment HV. Let C be the rotation of point V by angle 5pi/12 around point F. Let I be the line through points C and F. Point J is obtained by rotating point V by angle pi/4 about point C. Line T is the reflection of line I across point V. Point G is the midpoint of segment VF. Let B be the line through points G and J. Line M is the reflection of line T across line B. Point P is the reflection of point H across line B. Point X is the reflection of point H across line M. Find the length of segment XP. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.28", "dataset": "MATH"}
{"messages": [{"content": "LQ = 5. Point S is obtained by rotating point Q by angle pi about point L. Point E is obtained by rotating point S by angle 11pi/12 about point L. Point V is obtained by rotating point S by angle 5pi/6 about point Q. Let B be the midpoint of segment VE. Point R is obtained by rotating point V by angle 11pi/12 about point B. Point Z is the reflection of point E across segment QL. Point H is the reflection of point B across segment RZ. Let I be the midpoint of segment HB. Find the distance between points R and I. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.16", "dataset": "MATH"}
{"messages": [{"content": "ZA = 6. Let T be the rotation of point A by angle 11pi/12 around point Z. Point J is the midpoint of segment ZA. Let O be the rotation of point T by angle 5pi/12 around point Z. Let S be the midpoint of segment JO. Let D be the midpoint of segment ZO. Point C is the reflection of point A across segment ZO. Let E be the midpoint of segment DZ. Let G be the reflection of point C across point E. Find the length of segment SG. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.41", "dataset": "MATH"}
{"messages": [{"content": "LT = 3. Line C is the perpendicular bisector of segment TL. Point Z is on line C with |ZL| = 7. Let M be the line through point L parallel to line C. Line U is the reflection of line M across point T. Point F is the reflection of point Z across line U. Let X be the line through point F parallel to line U. Point W is the reflection of point T across line X. What is the length of segment WF? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.26", "dataset": "MATH"}
{"messages": [{"content": "MT = 1. Let Z be the perpendicular bisector of segment TM. Let C be the rotation of point M by angle 3pi/4 around point T. Let V be the midpoint of segment CT. Point E is the reflection of point C across line Z. Point K is the midpoint of segment VE. Point W is the reflection of point M across point K. Point P is the reflection of point K across point C. What is the length of segment PW? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.45", "dataset": "MATH"}
{"messages": [{"content": "Let EO = 7. Point X is the reflection of point E across point O. Line A is the perpendicular bisector of segment XO. Let N be the reflection of point O across point E. Point F is the reflection of point E across line A. Point J is obtained by rotating point X by angle 7pi/12 about point F. Let Q be the rotation of point E by angle pi/6 around point O. Let K be the angle bisector of angle JEQ. Point L is the reflection of point Q across line K. Point R is the reflection of point N across point Q. Point U is the reflection of point L across segment JN. What is the length of segment RU? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.89", "dataset": "MATH"}
{"messages": [{"content": "MI = 4. Let B be the midpoint of segment MI. Point E is the reflection of point B across point I. Let K be the angle bisector of angle MBI. Point L is the midpoint of segment BI. Point X is obtained by rotating point M by angle pi/3 about point L. Line Q is the perpendicular bisector of segment LX. Line R is the reflection of line Q across line K. Point H is the intersection of segment LX and line R. What is the length of segment EH? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.61", "dataset": "MATH"}
{"messages": [{"content": "Let JU = 6. Point R is obtained by rotating point J by angle 5pi/12 about point U. Point F is the reflection of point J across point U. Point G is the midpoint of segment RF. Let H be the angle bisector of angle JGF. Let C be the line through point U perpendicular to line H. Let D be the line through point F perpendicular to line C. Point Q is the midpoint of segment UJ. Point T is the reflection of point Q across line D. What is the distance between points T and G? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.58", "dataset": "MATH"}
{"messages": [{"content": "OI = 4. Let A be the rotation of point O by angle 5pi/12 around point I. Point F is the midpoint of segment OA. Point Q is the reflection of point O across segment AI. Let L be the line through point I perpendicular to segment OF. Point X is the reflection of point Q across line L. Let R be the reflection of point Q across point X. Point B is the reflection of point R across segment OF. Find the distance between points B and Q. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.52", "dataset": "MATH"}
{"messages": [{"content": "Let XG = 12. Let Z be the midpoint of segment XG. Let A be the rotation of point Z by angle 7pi/12 around point X. Point I is the reflection of point A across point G. Point H is the reflection of point Z across point A. Line P is the angle bisector of angle HGX. Point R is the reflection of point I across line P. Line J is the perpendicular bisector of segment AZ. Let F be the reflection of line P across line J. Point W is the reflection of point R across line F. Line M is the angle bisector of angle IHX. Point D is the reflection of point Z across line P. Point K is the reflection of point W across line M. What is the distance between points D and K? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.96", "dataset": "MATH"}
{"messages": [{"content": "TD = 7. Let N be the reflection of point T across point D. Let Y be the rotation of point N by angle 5pi/12 around point D. Let V be the reflection of point D across point Y. Let S be the line through points N and V. Let Z be the line through point Y parallel to line S. Point P is the reflection of point N across line Z. What is the length of segment VP? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.5", "dataset": "MATH"}
{"messages": [{"content": "Let RT = 9. Point K is obtained by rotating point R by angle 7pi/12 about point T. Point V is obtained by rotating point K by angle 5pi/6 about point T. Let F be the rotation of point K by angle pi around point T. Point Q is the midpoint of segment VT. Let W be the midpoint of segment TR. Let L be the line through point W perpendicular to segment TR. Point N is the reflection of point F across line L. Point O is the midpoint of segment NT. What is the measure of angle WOQ, in radians? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.83", "dataset": "MATH"}
{"messages": [{"content": "Let XF = 2. Let U be the midpoint of segment XF. Point K is obtained by rotating point F by angle 7pi/12 about point U. Line T passes through points F and K. Point M is the midpoint of segment XK. Point V is the reflection of point M across line T. Let P be the midpoint of segment UM. Find the distance between points V and P. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.28", "dataset": "MATH"}
{"messages": [{"content": "LX = 7. Let C be the perpendicular bisector of segment LX. Point A is on line C with |AL| = 8. Let W be the angle bisector of angle XLA. Point T is the reflection of point X across line W. Point D is the midpoint of segment TA. Let Q be the vector from point A to point D. Point P lies on line W. Let J be the angle bisector of angle DAT. Point F is the midpoint of segment TL. Point E is the translation of point P by vector Q. Point O is the midpoint of segment XP. Let Y be the line through point E parallel to line J. Line I is the reflection of line W across line Y. Line Z is the reflection of line W across point A. Point G is the reflection of point F across point O. Point H is the intersection of lines I and Z. What is the distance between points G and H? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.36", "dataset": "MATH"}
{"messages": [{"content": "UQ = 9. Point D is the reflection of point Q across point U. Line N is the perpendicular bisector of segment DQ. Let V be the vector from point Q to point D. Let J be the line through point Q parallel to line N. Let S be the midpoint of segment QU. Line K is the perpendicular bisector of segment QS. Point M is the midpoint of segment UD. Let C be point M translated by vector V. Point A is on line N with |AQ| = 6. Point W is the midpoint of segment UC. Line Y passes through point W parallel to line K. Line X passes through point A perpendicular to line Y. Let L be the reflection of line X through point Q. Point G is the reflection of point D across line L. Point P is the reflection of point A across line J. Find the distance between points P and G. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32.45", "dataset": "MATH"}
{"messages": [{"content": "KY = 4. Let B be the rotation of point Y by angle pi/12 around point K. Point R is the midpoint of segment KY. Point P is the reflection of point B across point K. Let M be the reflection of point P across point R. Let D be the reflection of point B across point R. Let X be the reflection of point D across point P. Let A be the angle bisector of angle DRX. Line J is the reflection of line A across point K. Point U is the reflection of point K across point M. Point C is the reflection of point R across line J. Let E be the midpoint of segment UB. Let L be the line through points C and P. Point G is obtained by rotating point M by angle 7pi/12 about point D. Line N is the perpendicular bisector of segment YP. Point T is the reflection of point C across line N. Point O is the reflection of point G across point T. Point V is the intersection of segment ET and line L. What is the distance between points O and V? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.95", "dataset": "MATH"}
{"messages": [{"content": "CA = 2. Point G is the midpoint of segment AC. Point T is obtained by rotating point G by angle 2pi/3 about point A. Let Z be the midpoint of segment TG. Point U is the reflection of point Z across point C. Let L be the midpoint of segment TU. What is the distance between points G and L? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.66", "dataset": "MATH"}
{"messages": [{"content": "Let CH = 1. Line P is the perpendicular bisector of segment HC. Point N lies on line P at distance 10 from point C. Let M be the midpoint of segment NH. Let D be the reflection of line P through point H. Let B be the reflection of line D through point M. Let U be the perpendicular bisector of segment MC. Line J passes through point M perpendicular to line B. Point W is the reflection of point N across point H. Point O is the reflection of point W across line J. Point E is the reflection of point N across line J. Point F is the midpoint of segment WO. Point L is the reflection of point F across segment NH. Point Z is the reflection of point E across line U. What is the distance between points L and Z? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "Let DG = 1. Let P be the rotation of point D by angle pi/12 around point G. Let U be the midpoint of segment DP. Let Y be the midpoint of segment DG. Let Q be the line through points Y and G. Point W is the reflection of point U across line Q. What is the measure of angle YWU, in radians? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.31", "dataset": "MATH"}
{"messages": [{"content": "WJ = 5. Point T is the midpoint of segment WJ. Line I is the perpendicular bisector of segment JW. Let P be the rotation of point T by angle 7pi/12 around point W. Let Q be the midpoint of segment JT. Point Z is the midpoint of segment QP. Line R passes through point Z parallel to line I. Let F be the reflection of point Z across point W. Line R and segment JW intersect at point K. Find the length of segment FK. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.33", "dataset": "MATH"}
{"messages": [{"content": "YD = 9. Let S be the rotation of point Y by angle pi/12 around point D. Point F is the midpoint of segment YS. Let Z be the perpendicular bisector of segment YF. Point V is obtained by rotating point D by angle pi/6 about point F. Point Q is the reflection of point F across point Y. Line H passes through point V parallel to line Z. Point U is the reflection of point Q across line H. Let C be the reflection of point F across point V. Find the distance between points U and C. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.63", "dataset": "MATH"}
{"messages": [{"content": "Let BC = 6. Let G be the vector from point C to point B. Let O be the midpoint of segment BC. Let V be point B translated by vector G. Point M is obtained by rotating point V by angle 11pi/12 about point O. Point P is obtained by rotating point C by angle 5pi/12 about point V. Let Q be the reflection of point M across point O. Point I is obtained by rotating point Q by angle 3pi/4 about point B. Let W be the reflection of point I across point B. Line S is the perpendicular bisector of segment PO. Point X is the reflection of point V across point W. Let L be the reflection of line S through point V. Point D is the reflection of point V across line L. Line N passes through point D parallel to line L. Point F is the intersection of line N and segment BC. Point R is the reflection of point W across segment BC. Point E is the midpoint of segment XF. Find the length of segment RE. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.54", "dataset": "MATH"}
{"messages": [{"content": "Let VD = 6. Point A is the midpoint of segment VD. Point S is obtained by rotating point V by angle pi/6 about point A. Point F is the reflection of point S across segment VD. Point M is the midpoint of segment VS. Let T be the midpoint of segment MF. Find the length of segment TS. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.88", "dataset": "MATH"}
{"messages": [{"content": "Let VJ = 11. Line A passes through points V and J. Point Z is obtained by rotating point J by angle 5pi/12 about point V. Point U is the reflection of point Z across line A. Line W passes through points Z and J. Let B be the rotation of point Z by angle 7pi/12 around point U. Let X be the perpendicular bisector of segment VU. Let I be the reflection of line W across line X. Point Y is the reflection of point U across line I. What is the length of segment BY? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37.97", "dataset": "MATH"}
{"messages": [{"content": "LO = 2. Line Y is the perpendicular bisector of segment OL. Let E be the rotation of point L by angle 5pi/6 around point O. Point D is obtained by rotating point L by angle pi/2 about point O. Point G is the reflection of point D across point L. Point F is the midpoint of segment DO. Point I is the reflection of point D across line Y. Let J be the perpendicular bisector of segment FE. Let M be the reflection of point D across point I. Line H is the reflection of line J across point G. Point T is the midpoint of segment IG. Point Q is the reflection of point M across line H. Find the distance between points Q and T. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.92", "dataset": "MATH"}
{"messages": [{"content": "HL = 4. Let I be the line through points H and L. Let X be the line through point L perpendicular to line I. Point M is obtained by rotating point L by angle 11pi/12 about point H. Line B passes through point M parallel to line X. Point R is the reflection of point H across point M. Lines I and B intersect at point Q. Point F is the reflection of point R across point Q. What is the length of segment RF? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.77", "dataset": "MATH"}
{"messages": [{"content": "Let MJ = 10. Point N is the midpoint of segment MJ. Let I be the reflection of point J across point M. Let V be the rotation of point J by angle pi/6 around point N. Let T be the midpoint of segment NJ. Point Q is the midpoint of segment VI. Point Z is the reflection of point N across segment VI. Point R is the midpoint of segment TZ. Let L be the reflection of point V across point R. Find the length of segment LQ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.01", "dataset": "MATH"}
{"messages": [{"content": "Let ZM = 1. B is constructed so that MB = 1. Point H is the reflection of point M across point Z. Line X passes through points H and B. C is placed 1 units away from B. Point I is the reflection of point Z across line X. Point F is the midpoint of segment IC. Let A be the midpoint of segment CH. Find the distance between points F and A. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "FU = 11. Let J be the rotation of point U by angle 11pi/12 around point F. Line N passes through points U and F. Point E is obtained by rotating point F by angle 3pi/4 about point J. Line Q passes through points E and U. Line Z is the reflection of line N across line Q. Let O be the reflection of line Q across line Z. Point R is the reflection of point F across point E. Point T is the reflection of point J across line O. What is the length of segment TR? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60.8", "dataset": "MATH"}
{"messages": [{"content": "WG = 11. Point S is the reflection of point G across point W. C is placed 11 units away from G. Let B be the reflection of point S across point G. Let Z be the reflection of point S across point B. Point O is the midpoint of segment ZC. Point E is the midpoint of segment CW. What is the distance between points O and E? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38.5", "dataset": "MATH"}
{"messages": [{"content": "Let ZI = 5. Point V is the reflection of point Z across point I. Let A be the reflection of point I across point V. Let E be the midpoint of segment IV. What is the distance between points A and E? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.5", "dataset": "MATH"}
{"messages": [{"content": "Let UY = 7. Let O be the reflection of point Y across point U. Let G be the rotation of point O by angle 7pi/12 around point U. Let M be the midpoint of segment UG. Let W be the reflection of point O across point G. Point K is the midpoint of segment WG. Find the distance between points K and M. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.6", "dataset": "MATH"}
{"messages": [{"content": "Let TX = 6. Point P is obtained by rotating point T by angle 5pi/6 about point X. Point J is the midpoint of segment XT. Let V be the midpoint of segment PX. Point K is the midpoint of segment VT. Let F be the midpoint of segment KT. Line L passes through point F perpendicular to segment PX. Let U be the line through point J perpendicular to line L. Point D is the midpoint of segment JT. Point Y is the reflection of point D across line U. Find the length of segment YP. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.93", "dataset": "MATH"}
{"messages": [{"content": "Let UB = 1. Point J is obtained by rotating point U by angle pi/4 about point B. Let Z be the reflection of point J across point U. Point V is the midpoint of segment BU. Line X is the angle bisector of angle ZBJ. Point H is the reflection of point V across line X. What is the distance between points H and Z? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.17", "dataset": "MATH"}
{"messages": [{"content": "OG = 5. Let V be the rotation of point G by angle pi around point O. Let M be the vector from point G to point V. Point W is the translation of point O by vector M. Let P be the rotation of point V by angle 5pi/6 around point G. Line D passes through points W and G. Point U is the midpoint of segment OG. Line E passes through point V perpendicular to line D. Line K is the reflection of line E across point U. Line H passes through point O parallel to line K. Lines K and D intersect at point F. Line N passes through points G and P. Point I is the intersection of lines H and N. Point J is the midpoint of segment IF. Find the distance between points I and J. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.2", "dataset": "MATH"}
{"messages": [{"content": "Let QX = 6. Point V is the reflection of point X across point Q. Let Y be the angle bisector of angle XQV. Line B passes through point V perpendicular to line Y. Let E be the line through point V parallel to line Y. Let S be the vector from point X to point V. Line J is the perpendicular bisector of segment VQ. Line O is the reflection of line E across line Y. Point I is the translation of point V by vector S. Point H is on line O. Let D be the reflection of line B through point H. Let F be the reflection of point V across point I. Let C be the midpoint of segment FX. Point K is the intersection of lines E and D. Line U is the reflection of line J across line Y. Lines U and D intersect at point M. Let R be the midpoint of segment CM. Let N be the midpoint of segment KF. What is the length of segment RN? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.5", "dataset": "MATH"}
{"messages": [{"content": "NY = 11. Let L be the reflection of point Y across point N. Line A passes through points Y and L. Let U be the reflection of point Y across point L. Let X be the angle bisector of angle UNY. Point P is obtained by rotating point L by angle 5pi/12 about point Y. Line G passes through point P perpendicular to line X. Let S be the rotation of point U by angle pi/12 around point P. Point F is the reflection of point Y across point U. Let E be the midpoint of segment FU. Point O is the reflection of point Y across line G. Point C is obtained by rotating point N by angle pi/6 about point L. Point B is the midpoint of segment EC. Line W is the angle bisector of angle SBU. Point Z is the reflection of point Y across line W. Let R be the midpoint of segment ON. Point T is the reflection of point R across line A. Find the distance between points T and Z. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39.78", "dataset": "MATH"}
{"messages": [{"content": "Let EY = 4. Point Q is the reflection of point E across point Y. Let B be the rotation of point Q by angle 5pi/12 around point E. Point O is the midpoint of segment YQ. Point R is the midpoint of segment YO. Point X is the reflection of point R across segment YB. Let C be the line through point O parallel to segment YB. Point D is the reflection of point X across line C. Point F is the reflection of point R across point D. Find the distance between points X and F. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.7", "dataset": "MATH"}
{"messages": [{"content": "XE = 7. Let H be the rotation of point E by angle 11pi/12 around point X. Point W is obtained by rotating point X by angle pi about point H. Point K is the reflection of point X across point W. Point A is the reflection of point E across point W. Let O be the line through points A and W. Point C is the reflection of point K across line O. Find the distance between points K and C. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.43", "dataset": "MATH"}
{"messages": [{"content": "XJ = 4. Let C be the line through point J perpendicular to segment XJ. Let S be the rotation of point X by angle 5pi/12 around point J. Let Z be the rotation of point J by angle pi/6 around point X. Let R be the reflection of line C through point Z. Let P be the reflection of line C across line R. Let N be the line through point S perpendicular to line R. Line P and segment XJ intersect at point Q. Let W be the reflection of point Q across point Z. Point H is the reflection of point Q across line N. What is the distance between points H and W? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.16", "dataset": "MATH"}
{"messages": [{"content": "Let FY = 6. Let A be the rotation of point Y by angle pi/12 around point F. Point M is the midpoint of segment FY. Let R be the reflection of point A across point M. Point U is the midpoint of segment MR. Point Z is the reflection of point F across point U. What is the length of segment ZA? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.04", "dataset": "MATH"}
{"messages": [{"content": "KV = 12. Point Y is obtained by rotating point V by angle pi/2 about point K. Let P be the midpoint of segment YV. Let N be the midpoint of segment PK. Let W be the perpendicular bisector of segment KY. Let A be the line through point K parallel to line W. Point C is obtained by rotating point P by angle pi/6 about point V. Point T is the reflection of point Y across line A. Let B be the reflection of point T across point N. Let F be the angle bisector of angle TCN. Point I is the midpoint of segment YK. Let L be the reflection of line F through point I. Point E is the intersection of segment YK and line L. Let G be the midpoint of segment EI. Point U is the midpoint of segment YG. What is the distance between points U and B? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.84", "dataset": "MATH"}
{"messages": [{"content": "Let ZB = 2. Point L is obtained by rotating point Z by angle 7pi/12 about point B. Let K be the midpoint of segment BL. Point S is the reflection of point K across segment LZ. Let F be the midpoint of segment ZK. Point V is the reflection of point K across segment SB. What is the distance between points V and F? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.31", "dataset": "MATH"}
{"messages": [{"content": "IY = 7. Let K be the vector from point I to point Y. Let A be point Y translated by vector K. Point M is obtained by rotating point Y by angle 5pi/6 about point I. Line E is the perpendicular bisector of segment YA. Point B is obtained by rotating point I by angle 3pi/4 about point Y. Let P be the midpoint of segment MA. Point Q is the reflection of point P across line E. Point V is the midpoint of segment BM. Find the distance between points Q and V. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.3", "dataset": "MATH"}
{"messages": [{"content": "BI = 1. Let E be the vector from point B to point I. Let H be the reflection of point I across point B. Point V is the translation of point I by vector E. Line R is the perpendicular bisector of segment BH. Point Y is on line R with |YI| = 11. Let J be the reflection of line R through point V. Line D passes through point Y parallel to segment BH. Point N is the reflection of point Y across segment BH. Let M be the line through points V and Y. Point A is the reflection of point V across line D. Let F be the reflection of line M across line J. Point L is the reflection of point N across line F. Find the length of segment AL. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35.85", "dataset": "MATH"}
{"messages": [{"content": "HK = 4. Point Y is the reflection of point K across point H. Point I is the reflection of point K across point Y. Line L is the perpendicular bisector of segment KI. Let C be the reflection of point Y across point K. Point S lies on line L at distance 5 from point Y. Point O is the midpoint of segment CS. Point P is the reflection of point C across line L. Point U is the midpoint of segment YO. Point R is the reflection of point U across segment SK. Find the distance between points P and R. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.34", "dataset": "MATH"}
{"messages": [{"content": "AV = 10. Point Y is the reflection of point A across point V. Point N is obtained by rotating point A by angle pi/2 about point V. Let K be the line through point Y perpendicular to segment AN. Point R is the reflection of point V across line K. Point S is the reflection of point R across segment AN. What is the measure of angle SVR, in radians? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.79", "dataset": "MATH"}
{"messages": [{"content": "Let VA = 9. Point J is the reflection of point A across point V. Let P be the rotation of point A by angle pi/6 around point J. Line D is the perpendicular bisector of segment JA. Let W be the reflection of point V across point A. Let O be the rotation of point W by angle 3pi/4 around point J. Point K is the midpoint of segment PO. Let Z be the reflection of line D through point K. Line T is the reflection of line Z across point J. Point I is the intersection of line T and segment JW. Find the length of segment PI. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.51", "dataset": "MATH"}
{"messages": [{"content": "Let QX = 7. Point T is the reflection of point X across point Q. Point I is the reflection of point Q across point X. Point W is the midpoint of segment QT. Point B is the reflection of point X across point I. Let V be the rotation of point B by angle pi/3 around point Q. Let C be the rotation of point X by angle pi/6 around point I. Point J is obtained by rotating point I by angle pi/2 about point W. Point L is the midpoint of segment WV. Point P is the reflection of point J across segment WV. Point Y is the reflection of point B across segment WV. Let A be the midpoint of segment LQ. Point F is the reflection of point Y across segment CP. Find the distance between points F and A. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40.71", "dataset": "MATH"}
{"messages": [{"content": "YV = 11. Point K is obtained by rotating point Y by angle pi/3 about point V. Let F be the reflection of point Y across point V. Line I passes through points F and Y. Let A be the reflection of line I through point K. Point B is the reflection of point K across line I. Point O is the reflection of point B across point V. Let L be the perpendicular bisector of segment VB. Let E be the reflection of line L across line A. Line P is the reflection of line E across point O. Point S is the reflection of point B across line P. What is the distance between points Y and S? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55.0", "dataset": "MATH"}
{"messages": [{"content": "Let BI = 2. Point M is the midpoint of segment BI. Point Y is the midpoint of segment MI. Let S be the rotation of point Y by angle pi/2 around point M. Let P be the rotation of point S by angle pi/12 around point B. Point F is obtained by rotating point Y by angle pi about point P. Let R be the line through points P and S. Let T be the line through points Y and P. Point W is the reflection of point B across line T. Let X be the reflection of line R through point W. Point C is the midpoint of segment PM. Point A is the reflection of point F across line X. What is the distance between points A and C? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.89", "dataset": "MATH"}
{"messages": [{"content": "Let EC = 6. Let X be the reflection of point E across point C. Point R is obtained by rotating point X by angle 3pi/4 about point E. Point U is the reflection of point R across point C. Line Y passes through points E and R. Point V is the reflection of point U across line Y. Let T be the midpoint of segment XR. Let Q be the line through points X and T. Point G is the reflection of point V across line Q. What is the length of segment EG? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29.39", "dataset": "MATH"}
{"messages": [{"content": "PT = 1. Let X be the rotation of point P by angle 5pi/12 around point T. Point I is the reflection of point T across point X. Let A be the reflection of point P across point T. Line R is the angle bisector of angle IXA. Line U passes through points I and P. Line N passes through point T parallel to line R. Point M is obtained by rotating point A by angle 7pi/12 about point I. Line G passes through point T parallel to line U. Line O is the reflection of line G across line N. Let E be the reflection of line N through point M. Lines E and O intersect at point W. Point K is the midpoint of segment AW. Let J be the midpoint of segment IA. What is the length of segment JK? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.22", "dataset": "MATH"}
{"messages": [{"content": "Let VC = 7. Let O be the midpoint of segment VC. Let X be the reflection of point O across point V. Point Z is the midpoint of segment VX. Point D is the reflection of point Z across point O. Find the distance between points D and V. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.75", "dataset": "MATH"}
{"messages": [{"content": "DO = 8. Line Q is the perpendicular bisector of segment OD. Point I lies on line Q at distance 3 from point D. Line S passes through point O parallel to line Q. Let F be the vector from point I to point O. Point A is the translation of point D by vector F. Point H is the reflection of point D across point A. Line N is the perpendicular bisector of segment IH. Let U be the reflection of line S across line N. Let B be the reflection of line N through point D. Point J is the intersection of lines B and U. What is the length of segment AJ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.27", "dataset": "MATH"}
{"messages": [{"content": "NX = 1. Let U be the vector from point N to point X. Let E be the rotation of point X by angle 7pi/12 around point N. Point B is obtained by rotating point E by angle 7pi/12 about point X. Let I be the rotation of point E by angle 7pi/12 around point B. Let H be point E translated by vector U. Let Z be the vector from point N to point I. Point S is the translation of point H by vector Z. Point W is the midpoint of segment SH. Line A passes through points X and N. Point V is the intersection of segment IH and line A. Point G is the reflection of point W across line A. Point P is obtained by rotating point V by angle pi/6 about point H. Line R passes through points X and W. Point D is the reflection of point G across line R. Let L be the midpoint of segment PG. What is the length of segment LD? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.12", "dataset": "MATH"}
{"messages": [{"content": "Let JR = 7. Let H be the line through points J and R. Point B is obtained by rotating point R by angle pi/6 about point J. Point G is the midpoint of segment BR. Line F is the perpendicular bisector of segment JG. Let T be the reflection of line F across line H. Line D is the reflection of line H across line T. Point I is the intersection of lines T and D. Line D and segment JB intersect at point Z. What is the distance between points Z and I? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.02", "dataset": "MATH"}
{"messages": [{"content": "LX = 9. Let P be the vector from point X to point L. Let Q be point L translated by vector P. Let S be the rotation of point Q by angle 11pi/12 around point X. Let T be the perpendicular bisector of segment QL. Let G be the midpoint of segment XL. Point E is the reflection of point S across line T. Find the distance between points E and G. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40.16", "dataset": "MATH"}
{"messages": [{"content": "Let EN = 3. Let V be the rotation of point N by angle pi/3 around point E. Let F be the rotation of point V by angle 3pi/4 around point E. Let H be the rotation of point E by angle pi/12 around point F. Line I passes through points H and E. Point G is the reflection of point E across point H. Line R passes through point F parallel to line I. Line D is the reflection of line I across line R. Point Z is the reflection of point G across line D. Point K is the midpoint of segment NZ. What is the distance between points Z and K? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.46", "dataset": "MATH"}
{"messages": [{"content": "Let TD = 8. Let J be the midpoint of segment TD. Let C be the perpendicular bisector of segment JT. Point U is on line C with |UJ| = 10. Point Q is the midpoint of segment DJ. Let I be the perpendicular bisector of segment QT. Line K is the reflection of line I across point U. Point V is obtained by rotating point Q by angle pi/4 about point D. Segment VT and line K intersect at point A. Let P be the midpoint of segment JA. Point N is the reflection of point Q across point P. Point M is the midpoint of segment PJ. Find the length of segment NM. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.25", "dataset": "MATH"}
{"messages": [{"content": "Let BE = 11. Let N be the line through points B and E. Point S is obtained by rotating point E by angle pi/2 about point B. Point T is the reflection of point S across line N. Point X lies on line N at distance 1 from point S. Point M is the midpoint of segment XT. Let L be the midpoint of segment MB. Let A be the midpoint of segment SL. Point D is the intersection of segments AT and MB. Find the distance between points D and A. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.04", "dataset": "MATH"}
{"messages": [{"content": "HP = 10. Point C is the reflection of point H across point P. Point L is obtained by rotating point P by angle 5pi/6 about point C. Point G is obtained by rotating point H by angle 7pi/12 about point L. Line B passes through points G and H. Point V is the reflection of point G across point C. Point K is the reflection of point C across line B. Let U be the reflection of point K across point V. Find the distance between points U and K. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "109.81", "dataset": "MATH"}
{"messages": [{"content": "Let MV = 1. Point F is the midpoint of segment MV. Let E be the angle bisector of angle MFV. Point U is on line E. Point B is the midpoint of segment MF. Let K be the midpoint of segment UV. Let C be the midpoint of segment BU. What is the distance between points K and C? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.38", "dataset": "MATH"}
{"messages": [{"content": "BV = 8. Let Q be the vector from point B to point V. Let X be the vector from point B to point V. Point G is the midpoint of segment BV. Let O be the rotation of point G by angle pi/12 around point V. Let M be point O translated by vector X. Point H is the translation of point V by vector Q. Point E is the reflection of point M across segment BV. Point Y is the reflection of point M across segment EG. Point U is the midpoint of segment EG. Point J is the reflection of point H across point U. What is the distance between points J and Y? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.66", "dataset": "MATH"}
{"messages": [{"content": "Let FX = 2. Let K be the reflection of point X across point F. Point U is the midpoint of segment FX. Let S be the reflection of point X across point K. Point Q is obtained by rotating point K by angle pi/6 about point U. Let T be the midpoint of segment QU. Line J is the perpendicular bisector of segment FS. Let Y be the line through point T parallel to line J. Point L is the reflection of point F across point S. Point Z is the reflection of point L across line Y. Point A is the reflection of point T across segment FX. Find the length of segment ZA. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.72", "dataset": "MATH"}
{"messages": [{"content": "RF = 11. Let W be the rotation of point R by angle 7pi/12 around point F. Let T be the midpoint of segment RW. Let J be the midpoint of segment RT. Let RL = 8. Line X is the angle bisector of angle RJL. Line Z is the perpendicular bisector of segment WJ. Point D is the reflection of point T across line Z. Point C is the reflection of point D across line X. Find the length of segment JC. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.73", "dataset": "MATH"}
{"messages": [{"content": "Let GC = 9. Let Y be the rotation of point G by angle pi around point C. Line U is the perpendicular bisector of segment YC. Point N lies on segment CY. Point I lies on line U at distance 8 from point G. Point A is the reflection of point G across line U. Let Q be the reflection of point I across point N. Let J be the angle bisector of angle GNY. Point V is the reflection of point Q across line J. What is the length of segment AV? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.69", "dataset": "MATH"}
{"messages": [{"content": "Let WD = 8. Line N is the perpendicular bisector of segment WD. Point A is the midpoint of segment WD. Point U is the midpoint of segment DA. Line F is the reflection of line N across point W. Let G be the reflection of point U across point D. Let T be the rotation of point U by angle 11pi/12 around point W. Point I is the midpoint of segment UT. Let R be the reflection of point U across point G. Point Z is the midpoint of segment IR. Let V be the reflection of line N across line F. Line O passes through point Z parallel to segment TA. Point L is the intersection of lines V and O. Find the distance between points U and L. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.32", "dataset": "MATH"}
{"messages": [{"content": "Let PD = 5. Point V is obtained by rotating point P by angle 5pi/6 about point D. Let I be the midpoint of segment VP. Point S is the midpoint of segment VD. Point O is the reflection of point D across point I. Find the distance between points S and O. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Let JE = 3. Let X be the rotation of point E by angle 3pi/4 around point J. Let B be the rotation of point X by angle 3pi/4 around point E. Let D be the reflection of point X across point B. Point T is the reflection of point J across point B. Let R be the reflection of point T across point J. Let K be the perpendicular bisector of segment XR. Let S be the reflection of line K through point E. Point O is the reflection of point D across line S. Find the distance between points O and R. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.97", "dataset": "MATH"}
{"messages": [{"content": "NI = 10. Let H be the midpoint of segment NI. Line C is the perpendicular bisector of segment IN. Point P is obtained by rotating point H by angle pi/2 about point N. Point W is obtained by rotating point H by angle pi/3 about point N. Point X is the reflection of point N across point P. Let Y be the rotation of point X by angle 3pi/4 around point W. Let U be the perpendicular bisector of segment WH. Line O is the reflection of line U across point X. Let A be the line through point P parallel to line O. Let V be the line through point X perpendicular to line C. Point Z is the reflection of point X across line A. Line K is the reflection of line V across point Z. Point B is the reflection of point Y across line K. Let T be the midpoint of segment ZB. What is the distance between points T and X? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.23", "dataset": "MATH"}
{"messages": [{"content": "Let DF = 6. Let X be the midpoint of segment FD. Point Z is obtained by rotating point X by angle pi/12 about point D. Let K be the reflection of point X across point D. Point B is the reflection of point D across segment XZ. Line L is the perpendicular bisector of segment KD. Point I is the reflection of point B across line L. Find the measure of angle XBI, in radians. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.26", "dataset": "MATH"}
{"messages": [{"content": "XO = 3. Point W is the reflection of point X across point O. Point A is the reflection of point X across point W. Let P be the rotation of point O by angle 7pi/12 around point W. Line D passes through point A perpendicular to segment XW. Let B be the reflection of point P across point W. Point H is obtained by rotating point X by angle pi/6 about point O. Let L be the perpendicular bisector of segment HW. Let Q be the reflection of line L through point P. Let G be the reflection of point X across point B. Point I is the reflection of point G across segment XW. Line C is the reflection of line D across line Q. Point K is the intersection of segment XW and line C. What is the distance between points I and K? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.6", "dataset": "MATH"}
{"messages": [{"content": "Let JS = 4. Let B be the rotation of point J by angle pi/3 around point S. Let C be the midpoint of segment JS. Let G be the rotation of point B by angle pi/4 around point J. Let L be the rotation of point B by angle 5pi/12 around point C. Let F be the perpendicular bisector of segment BG. Let W be the line through points J and L. Let H be the reflection of line F across line W. Point V is the midpoint of segment SC. Point P is the midpoint of segment VJ. Point E is the reflection of point B across line H. Find the distance between points P and E. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.44", "dataset": "MATH"}
{"messages": [{"content": "YP = 2. Let M be the reflection of point Y across point P. Point R is the midpoint of segment YP. Let Q be the rotation of point Y by angle 3pi/4 around point R. Let V be the perpendicular bisector of segment QP. Line U is the perpendicular bisector of segment MQ. Let L be the midpoint of segment QY. Let N be the reflection of line U across line V. Line Z is the reflection of line U across line N. Let K be the rotation of point Q by angle 3pi/4 around point L. Line H passes through point K parallel to line Z. Point T is the intersection of lines H and N. Point W is the reflection of point T across line Z. Point I is the midpoint of segment MR. Find the length of segment WI. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.25", "dataset": "MATH"}
{"messages": [{"content": "CM = 2. Let U be the line through points M and C. Let X be the rotation of point M by angle pi/6 around point C. Let B be the reflection of line U through point X. Point N is the reflection of point X across line B. Let W be the line through points M and X. Lines B and W intersect at point R. What is the distance between points R and N? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.04", "dataset": "MATH"}
{"messages": [{"content": "Let LD = 2. Let F be the line through points L and D. Let M be the reflection of point L across point D. Point I is on line F. Point H is on line F with |HI| = 8. Point S lies on line F at distance 10 from point I. Let Y be the perpendicular bisector of segment SD. Point G is on line Y with |GH| = 8. Let R be the reflection of point G across point H. Let U be the midpoint of segment HR. Point T is the midpoint of segment MU. Point Q is the midpoint of segment UL. What is the distance between points Q and T? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "JB = 6. Point S is obtained by rotating point J by angle pi/3 about point B. Let E be the rotation of point S by angle pi/4 around point B. Let U be the midpoint of segment SJ. Line F passes through point J perpendicular to segment UB. Point N is the reflection of point E across line F. Line V passes through points B and J. Point L is the midpoint of segment UB. Point Y is the reflection of point N across segment UB. Let I be the reflection of point E across point N. Point D is the reflection of point L across line V. Line K is the angle bisector of angle LJI. Let G be the midpoint of segment NY. Point Q is the reflection of point D across line K. Find the length of segment GQ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.98", "dataset": "MATH"}
{"messages": [{"content": "LY = 1. Point P is obtained by rotating point L by angle pi about point Y. Let E be the rotation of point Y by angle 3pi/4 around point P. Let G be the line through points E and L. Let F be the line through point Y parallel to line G. Let I be the line through points L and P. Point J is the reflection of point L across segment PE. Let B be the line through point J parallel to line G. Point M is the midpoint of segment PE. Let H be the midpoint of segment EM. Let K be the reflection of line F across line B. Point R is the reflection of point E across line K. Point W is the reflection of point R across segment PE. Let T be the midpoint of segment WH. Point O is the intersection of lines I and K. What is the length of segment OT? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.25", "dataset": "MATH"}
{"messages": [{"content": "Let QW = 1. Let V be the midpoint of segment WQ. Point N is obtained by rotating point Q by angle pi/4 about point W. Let M be the midpoint of segment NV. Let R be the rotation of point W by angle 11pi/12 around point N. Point B is the reflection of point N across point R. Point C is the reflection of point Q across point R. Point U is the midpoint of segment CB. Line T is the angle bisector of angle RMV. Point G is the reflection of point U across line T. Point F is the midpoint of segment WG. What is the distance between points F and M? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.49", "dataset": "MATH"}
{"messages": [{"content": "GS = 8. Let K be the reflection of point G across point S. Let D be the midpoint of segment GS. Let F be the angle bisector of angle GDS. Point R is the midpoint of segment KD. Point Y is the midpoint of segment SR. Let Q be the reflection of line F through point Y. Point O lies on line Q. Point A is the reflection of point O across line F. Find the distance between points A and O. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.0", "dataset": "MATH"}
{"messages": [{"content": "Let OF = 5. Point N is the reflection of point F across point O. Let C be the vector from point F to point O. Let Q be the perpendicular bisector of segment FO. Point Y is the translation of point N by vector C. Let L be the reflection of point Y across point O. Line J passes through point F parallel to line Q. Let H be the reflection of line Q across line J. Let T be the line through point O parallel to line H. Point P is on line T with |PN| = 6. Point M is the reflection of point N across segment LP. Point U is the reflection of point M across segment FP. Point Z is the reflection of point U across point P. Find the length of segment LZ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.94", "dataset": "MATH"}
{"messages": [{"content": "IN = 12. Point E is obtained by rotating point I by angle 5pi/6 about point N. Let X be the midpoint of segment EN. Line A passes through point X perpendicular to segment IE. Point D is the midpoint of segment EX. Point O is obtained by rotating point D by angle 11pi/12 about point I. Let T be the midpoint of segment ON. Let Q be the angle bisector of angle OET. Point R is the reflection of point I across line Q. Point Y is the reflection of point R across line A. What is the length of segment YT? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38.24", "dataset": "MATH"}
{"messages": [{"content": "Let WF = 7. Let X be the vector from point F to point W. Point E is the translation of point W by vector X. Point I is obtained by rotating point W by angle pi/4 about point F. Let D be the rotation of point W by angle 11pi/12 around point E. Line Y passes through points W and D. Point G is the reflection of point I across point W. Let O be the rotation of point G by angle 5pi/6 around point E. Point M is the midpoint of segment DE. Point B is the midpoint of segment MG. Line V is the perpendicular bisector of segment BW. Point R is obtained by rotating point O by angle 2pi/3 about point M. Point H is the midpoint of segment RW. Line Y and segment HB intersect at point A. Point U is the reflection of point A across line V. Let K be the reflection of point B across point U. What is the length of segment KA? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.72", "dataset": "MATH"}
{"messages": [{"content": "Let KM = 5. Let V be the reflection of point M across point K. Let I be the reflection of point K across point V. Let P be the vector from point M to point I. Line C is the angle bisector of angle KVI. Point J is obtained by rotating point K by angle 5pi/12 about point M. Let U be point J translated by vector P. Line T is the perpendicular bisector of segment MI. Let O be the reflection of line T across line C. Line S is the reflection of line O across line T. Let F be the midpoint of segment MI. Point Y is the reflection of point F across line S. Find the length of segment UY. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.4", "dataset": "MATH"}
{"messages": [{"content": "Let JE = 8. Point W is obtained by rotating point E by angle pi/3 about point J. Point N is the midpoint of segment EJ. Point V is the reflection of point W across point E. Point B is the reflection of point V across point W. Point G is the midpoint of segment NB. Point L is the reflection of point G across segment WJ. Point P is the midpoint of segment LE. Segments WJ and NB intersect at point T. Find the length of segment PT. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.3", "dataset": "MATH"}
{"messages": [{"content": "Let ML = 2. Point G is obtained by rotating point M by angle 2pi/3 about point L. Point I is the midpoint of segment LG. Point T is the reflection of point I across point M. Point D is the reflection of point T across point I. Point F is the midpoint of segment ML. Let S be the reflection of point D across point F. Line P is the perpendicular bisector of segment ML. Point O is the reflection of point S across segment ML. Let K be the line through point O parallel to segment ML. Let E be the angle bisector of angle OMD. Point B is the reflection of point G across line P. Line Z is the reflection of line E across line K. Let X be the midpoint of segment TO. Point Q is the reflection of point X across line Z. Let W be the midpoint of segment QB. Find the length of segment WX. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.76", "dataset": "MATH"}
{"messages": [{"content": "Let KS = 12. Let O be the rotation of point K by angle 5pi/6 around point S. Line W is the angle bisector of angle KSO. Point B is obtained by rotating point K by angle pi about point O. Let F be the line through point B parallel to line W. Let A be the reflection of point K across point B. Let I be the midpoint of segment SA. Point N is the reflection of point A across line W. Let E be the reflection of line F across line W. Let X be the reflection of line W across line E. Let P be the midpoint of segment BI. Point M is the reflection of point N across line X. Let T be the line through points A and P. Line T and segment KS intersect at point G. Point Y is the reflection of point G across point S. What is the length of segment MY? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63.92", "dataset": "MATH"}
{"messages": [{"content": "QG = 7. Point B is obtained by rotating point Q by angle 2pi/3 about point G. Line I is the perpendicular bisector of segment GQ. Let J be the reflection of line I through point G. Let C be the reflection of line J across line I. Line M passes through point Q parallel to segment BG. Point N is the midpoint of segment BG. Point R is the reflection of point N across line M. Point E is the reflection of point Q across line C. Point W is the reflection of point E across point B. Point S is the reflection of point G across line M. Let L be the reflection of point W across point R. Point T is the reflection of point L across segment BG. Let D be the midpoint of segment ST. Find the length of segment DT. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25.24", "dataset": "MATH"}
{"messages": [{"content": "Let PN = 9. Point L is the reflection of point N across point P. Point W is obtained by rotating point L by angle 5pi/6 about point N. Point S is the midpoint of segment NW. Line J is the angle bisector of angle WPS. Point R is the midpoint of segment LW. Let O be the line through point W perpendicular to line J. Point Z is the reflection of point S across line O. Let B be the line through point Z perpendicular to segment PL. Point H is the reflection of point R across line B. Find the distance between points H and S. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42.52", "dataset": "MATH"}
{"messages": [{"content": "Let BH = 11. Line P passes through points H and B. Point G is obtained by rotating point B by angle 5pi/6 about point H. Let M be the reflection of point H across point B. Point I is the reflection of point G across line P. Let F be the midpoint of segment MI. Let U be the reflection of point H across point F. Find the distance between points M and U. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.0", "dataset": "MATH"}
{"messages": [{"content": "EC = 8. Let Q be the perpendicular bisector of segment CE. Let A be the rotation of point E by angle 5pi/12 around point C. Line V passes through point E parallel to line Q. Let I be the reflection of line V across line Q. Let K be the rotation of point E by angle 11pi/12 around point C. Point P is obtained by rotating point K by angle 7pi/12 about point E. Point R is the intersection of segment KP and line I. Point B is obtained by rotating point A by angle pi/12 about point R. Point U is the reflection of point K across line V. Point J is the reflection of point E across segment KP. Point M is the reflection of point B across segment JU. Find the distance between points M and A. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32.3", "dataset": "MATH"}
{"messages": [{"content": "RC = 2. Let B be the reflection of point C across point R. Line Z passes through points B and R. Point E is obtained by rotating point C by angle pi/4 about point R. Let U be the vector from point R to point B. Point A is the translation of point E by vector U. Let N be the line through point E parallel to line Z. Let Y be the reflection of line Z across line N. Let H be the rotation of point A by angle pi/6 around point R. Let W be the line through points B and E. Point O is the reflection of point H across line W. Point J is the reflection of point R across line Y. Let L be the midpoint of segment OJ. Let D be the midpoint of segment OL. What is the length of segment OD? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.45", "dataset": "MATH"}
{"messages": [{"content": "Let OG = 7. Let P be the midpoint of segment GO. Let X be the rotation of point O by angle 5pi/6 around point G. Point R is the midpoint of segment PX. Point M is obtained by rotating point G by angle pi/6 about point X. Let I be the midpoint of segment RX. Point T is the reflection of point O across point G. Point H is the reflection of point X across point T. Let B be the reflection of point M across point I. Point E is the reflection of point X across point H. Find the distance between points E and B. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.35", "dataset": "MATH"}
{"messages": [{"content": "Let HK = 7. Let M be the rotation of point H by angle pi/2 around point K. Let D be the midpoint of segment KH. Let I be the perpendicular bisector of segment DH. Line N is the reflection of line I across point K. Point L is the reflection of point M across line N. Find the distance between points L and H. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.85", "dataset": "MATH"}
{"messages": [{"content": "VZ = 8. Point K is the reflection of point V across point Z. Point E is obtained by rotating point V by angle 2pi/3 about point K. Let R be the vector from point V to point K. Let B be point E translated by vector R. Let F be the rotation of point Z by angle pi/3 around point V. Let T be the reflection of point B across point V. Let W be the reflection of point V across point F. Point C is the midpoint of segment TE. Let U be the midpoint of segment EC. Let N be the midpoint of segment UW. What is the distance between points N and U? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.39", "dataset": "MATH"}
{"messages": [{"content": "RQ = 11. Let D be the rotation of point Q by angle 11pi/12 around point R. Line B is the angle bisector of angle QDR. Let Y be the midpoint of segment DQ. Point N is the reflection of point Y across line B. Point F is the midpoint of segment YN. What is the distance between points N and F? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
{"messages": [{"content": "DW = 5. Let O be the rotation of point W by angle pi/2 around point D. Let I be the rotation of point D by angle pi/3 around point W. Let Q be the angle bisector of angle IWO. Point M is the midpoint of segment WO. Line P passes through point I perpendicular to line Q. Line S is the perpendicular bisector of segment OI. Let V be the reflection of line P across line S. Let G be the reflection of line V through point M. Point B is the reflection of point D across line G. Point X is the midpoint of segment WB. What is the length of segment OX? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.5", "dataset": "MATH"}
{"messages": [{"content": "Let SH = 2. Point Y is obtained by rotating point S by angle 5pi/12 about point H. Point R is obtained by rotating point S by angle 2pi/3 about point H. Let D be the rotation of point Y by angle 2pi/3 around point R. Point T is the reflection of point Y across point R. Let M be the reflection of point D across point T. Point L is the reflection of point Y across segment HS. Let G be the midpoint of segment LM. What is the distance between points G and D? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.91", "dataset": "MATH"}
{"messages": [{"content": "LE = 7. Let V be the midpoint of segment LE. Let S be the perpendicular bisector of segment VE. Line H passes through point E perpendicular to line S. Point J is obtained by rotating point L by angle pi/12 about point E. Line Z is the perpendicular bisector of segment EJ. Point O is the reflection of point V across line Z. Let X be the line through point O parallel to line H. Point K is the reflection of point O across point E. Point G is the reflection of point J across line X. Find the length of segment GK. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.62", "dataset": "MATH"}
{"messages": [{"content": "Let IH = 1. Point E is obtained by rotating point H by angle 7pi/12 about point I. Let X be the reflection of point I across point E. Let Z be the line through points H and X. Line L passes through point H perpendicular to line Z. Point W is the reflection of point X across line L. Find the distance between points W and X. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.91", "dataset": "MATH"}
{"messages": [{"content": "Let FQ = 7. Let X be the line through points Q and F. Point D is obtained by rotating point Q by angle 5pi/6 about point F. Point R is obtained by rotating point D by angle pi/12 about point F. Point W is obtained by rotating point F by angle pi/4 about point R. Let S be the reflection of line X through point D. Line B is the perpendicular bisector of segment WR. Line Z is the reflection of line B across line S. Let V be the line through point Q parallel to line B. Point G is the intersection of lines V and Z. What is the distance between points G and D? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.97", "dataset": "MATH"}
{"messages": [{"content": "Let GU = 9. Let P be the midpoint of segment GU. Let X be the midpoint of segment PU. Point I is obtained by rotating point X by angle pi/6 about point P. Let E be the perpendicular bisector of segment XU. Point T is the reflection of point G across line E. Line S passes through point P parallel to line E. Line L passes through point X perpendicular to line S. Point O is the reflection of point X across point T. Line F passes through point T perpendicular to line L. Let M be the rotation of point U by angle pi/6 around point T. Let R be the line through point I parallel to line L. Point J lies on line F at distance 10 from point O. Point Y is the reflection of point U across point M. Line N passes through point Y perpendicular to line R. Let A be the reflection of line N through point J. Point W is the intersection of lines R and A. Point H is the midpoint of segment TX. Find the distance between points W and H. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.51", "dataset": "MATH"}
{"messages": [{"content": "Let WY = 12. Let C be the reflection of point Y across point W. Let D be the midpoint of segment YW. Point R is obtained by rotating point C by angle 5pi/6 about point D. Point K is the reflection of point C across point D. Let O be the midpoint of segment YK. Let J be the midpoint of segment OR. Point N is the midpoint of segment WJ. Find the length of segment JN. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.15", "dataset": "MATH"}
{"messages": [{"content": "Let KV = 8. Let I be the rotation of point K by angle pi/6 around point V. Let T be the rotation of point K by angle 7pi/12 around point I. Point C is the reflection of point I across point T. Point A is the reflection of point C across segment KV. Point G is the reflection of point T across segment KV. Find the distance between points G and A. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.14", "dataset": "MATH"}
{"messages": [{"content": "Let QD = 1. Point Y is the midpoint of segment DQ. Point N is obtained by rotating point Q by angle 3pi/4 about point Y. Point O is the reflection of point Q across point D. Let V be the reflection of point O across point N. Point W is the reflection of point V across point Q. Point P is the reflection of point N across point W. Find the distance between points Y and P. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.93", "dataset": "MATH"}
{"messages": [{"content": "Let UW = 11. Point X is the reflection of point W across point U. Point I is obtained by rotating point W by angle pi/12 about point X. Let K be the midpoint of segment IU. Point R is the reflection of point U across segment KX. Let E be the midpoint of segment RI. Let H be the midpoint of segment RE. Find the length of segment RH. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.77", "dataset": "MATH"}
{"messages": [{"content": "Let LX = 4. Point T is the midpoint of segment LX. Let U be the vector from point T to point X. Point P is obtained by rotating point L by angle 5pi/6 about point X. Point C is the translation of point X by vector U. Point Z is the midpoint of segment XP. Point J is the reflection of point Z across segment TX. Let F be the line through point J perpendicular to segment PT. Point V is the reflection of point C across line F. Find the distance between points Z and V. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.65", "dataset": "MATH"}
{"messages": [{"content": "Let UM = 5. Let X be the midpoint of segment MU. Let C be the perpendicular bisector of segment UX. Point F is the reflection of point M across line C. Let D be the rotation of point M by angle 3pi/4 around point F. Line L is the perpendicular bisector of segment MU. Let I be the midpoint of segment DX. Point Q is the reflection of point I across segment MU. Line P is the reflection of line C across line L. Point R is the intersection of line P and segment MU. Find the length of segment RQ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.93", "dataset": "MATH"}
{"messages": [{"content": "Let BE = 9. Let Y be the line through points E and B. Point N is obtained by rotating point B by angle pi/6 about point E. Let P be the perpendicular bisector of segment EB. Point O is the reflection of point E across point N. Point I is the reflection of point O across line P. Point G is the reflection of point I across line Y. Find the measure of angle IGB, in radians. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.05", "dataset": "MATH"}
{"messages": [{"content": "Let HU = 7. Let O be the midpoint of segment UH. Let J be the vector from point O to point U. Line L is the perpendicular bisector of segment HO. Point V is on line L with |VH| = 11. Let Y be the reflection of point H across point U. Point T is the translation of point Y by vector J. Line S passes through point T perpendicular to segment HO. Point P is the midpoint of segment VT. Line W passes through points U and P. Line G is the reflection of line W across line S. Point D is the reflection of point V across line G. Find the distance between points H and D. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45.16", "dataset": "MATH"}
{"messages": [{"content": "Let PK = 3. Point F is the midpoint of segment KP. Let G be the rotation of point K by angle pi/4 around point F. Let W be the line through point P perpendicular to segment PK. Let Q be the line through point G parallel to segment PK. Point T is the reflection of point P across point G. Line X is the reflection of line W across point T. Point E is the reflection of point K across line X. Point J is the reflection of point E across line Q. What is the length of segment JE? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.12", "dataset": "MATH"}
{"messages": [{"content": "BU = 9. Let W be the midpoint of segment UB. Point T is the midpoint of segment UW. Let A be the reflection of point T across point W. Find the distance between points A and B. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "Let HE = 7. Point M is the midpoint of segment HE. Let V be the vector from point E to point H. Let R be the perpendicular bisector of segment HE. Point S lies on line R at distance 9 from point H. Let X be the line through points H and S. Point T is the translation of point M by vector V. Point N is on line R. Let C be point H translated by vector V. Line O passes through point N parallel to line X. Point W is the reflection of point C across line O. Point A is the reflection of point T across segment WC. Point D is the midpoint of segment ST. What is the length of segment DA? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.16", "dataset": "MATH"}
{"messages": [{"content": "CX = 10. Let E be the reflection of point X across point C. Point Z is obtained by rotating point C by angle pi/4 about point X. Point Y is the reflection of point E across segment CZ. Point M is the midpoint of segment YC. Point L is the midpoint of segment CM. Point R is the reflection of point Y across segment MZ. What is the distance between points R and L? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.84", "dataset": "MATH"}
{"messages": [{"content": "Let VS = 10. Line C passes through points V and S. Point X is the reflection of point V across point S. Let N be the reflection of point X across point V. Line U passes through point N perpendicular to line C. Point K is the reflection of point S across line U. Find the distance between points N and K. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30.0", "dataset": "MATH"}
{"messages": [{"content": "AY = 7. Point D is obtained by rotating point A by angle 7pi/12 about point Y. Let T be the vector from point Y to point A. Let U be point D translated by vector T. Line F is the angle bisector of angle AYD. Point Q is obtained by rotating point A by angle pi/2 about point D. Line O is the angle bisector of angle DYU. Let C be the line through point Q parallel to line F. Let E be the reflection of line C across line O. Lines C and E intersect at point X. What is the distance between points X and U? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.19", "dataset": "MATH"}
{"messages": [{"content": "TN = 6. Let A be the rotation of point T by angle pi/6 around point N. Let F be the reflection of point A across point N. Let Q be the reflection of point A across point F. Let R be the reflection of point N across point Q. Let S be the angle bisector of angle TRQ. Point J is the reflection of point N across line S. Find the length of segment AJ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.63", "dataset": "MATH"}
{"messages": [{"content": "Let QZ = 9. Let R be the rotation of point Q by angle pi/4 around point Z. Let O be the rotation of point Q by angle 3pi/4 around point Z. Let S be the reflection of point R across point Q. Let D be the midpoint of segment SZ. Point J is the reflection of point D across segment OQ. Line W is the perpendicular bisector of segment JQ. Point T is the reflection of point Z across line W. Let M be the reflection of point D across point T. Find the length of segment MT. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.64", "dataset": "MATH"}
{"messages": [{"content": "EU = 10. Let X be the midpoint of segment EU. Line G passes through points E and X. Line V passes through point E perpendicular to line G. Let Y be the midpoint of segment XE. Point J is on line V with |JU| = 3. Point L is the reflection of point X across point U. Point K is the reflection of point J across point X. Point A is the midpoint of segment LK. Let P be the reflection of point A across point Y. What is the distance between points P and Y? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.11", "dataset": "MATH"}
{"messages": [{"content": "Let YL = 12. Let M be the vector from point Y to point L. Let E be point L translated by vector M. Point X is obtained by rotating point L by angle 11pi/12 about point Y. Let I be the reflection of point E across point Y. Let N be the angle bisector of angle IXY. Let T be the line through point Y parallel to line N. Point W is the reflection of point L across line T. Find the length of segment EW. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36.0", "dataset": "MATH"}
{"messages": [{"content": "Let GO = 7. Let S be the rotation of point O by angle 7pi/12 around point G. Let W be the perpendicular bisector of segment GO. Line T is the reflection of line W across point S. Line I is the reflection of line T across line W. Point D is the reflection of point S across line I. Point B is the midpoint of segment GO. Let Q be the midpoint of segment DB. What is the distance between points S and Q? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.9", "dataset": "MATH"}
{"messages": [{"content": "US = 9. Let R be the midpoint of segment SU. Point O is the midpoint of segment RS. Let Q be the rotation of point S by angle pi/2 around point R. Point K is the reflection of point O across segment QS. Let C be the line through points R and K. Point P is the intersection of segment QS and line C. Point V is the midpoint of segment PK. Find the distance between points V and O. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
{"messages": [{"content": "NZ = 1. Point S is obtained by rotating point Z by angle 7pi/12 about point N. Point K is the reflection of point N across segment ZS. Point L is the midpoint of segment SN. Point F is the reflection of point L across point S. Find the distance between points F and K. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
{"messages": [{"content": "IT = 7. Let G be the rotation of point I by angle 7pi/12 around point T. Let P be the reflection of point T across point G. Point U is the reflection of point P across point I. Line K is the perpendicular bisector of segment IP. Let R be the line through point U parallel to line K. Point Z is the reflection of point G across line K. Let B be the reflection of line R across line K. Line Y passes through point Z perpendicular to line B. Line L passes through point G perpendicular to line Y. Let N be the reflection of point T across point Z. Point M is the reflection of point U across line L. Point V is the reflection of point Z across segment IG. Point X is the reflection of point M across point U. Let Q be the reflection of point N across point V. What is the distance between points X and Q? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78.51", "dataset": "MATH"}
{"messages": [{"content": "Let UT = 4. Point L is obtained by rotating point T by angle 5pi/12 about point U. Line J passes through points U and L. Point H is the reflection of point T across line J. Let O be the reflection of point U across point L. Point E is the reflection of point U across point O. What is the distance between points E and H? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.46", "dataset": "MATH"}
{"messages": [{"content": "SW = 4. Line T is the perpendicular bisector of segment SW. Point F is the reflection of point S across point W. Point U lies on line T at distance 7 from point F. Point M is obtained by rotating point F by angle pi/3 about point W. Let L be the line through point M perpendicular to line T. Point Y is the reflection of point U across line L. Point V is obtained by rotating point M by angle pi/3 about point Y. Point O is the midpoint of segment SW. Point C is the reflection of point O across segment VU. Let N be the midpoint of segment VU. Find the length of segment CN. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.1", "dataset": "MATH"}
{"messages": [{"content": "KD = 2. Let U be the perpendicular bisector of segment KD. Point F is the reflection of point D across point K. Point T is obtained by rotating point F by angle 11pi/12 about point D. Let E be the line through point D parallel to line U. Let Z be the rotation of point K by angle pi/12 around point T. Point C is obtained by rotating point K by angle pi/2 about point F. Line H is the reflection of line E across line U. Point W is the reflection of point C across line U. Point J is the reflection of point W across line H. Point M is the midpoint of segment ZJ. Let B be the reflection of point M across point K. Find the distance between points B and M. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.09", "dataset": "MATH"}
{"messages": [{"content": "Let OB = 8. Point G is the midpoint of segment OB. M is constructed so that BM = 5. Let P be the midpoint of segment BM. Point Z is the midpoint of segment BP. Let X be the midpoint of segment PO. Point L is the reflection of point X across segment ZG. What is the length of segment ZL? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Let GJ = 3. Let N be the rotation of point G by angle 3pi/4 around point J. Let C be the reflection of point G across point J. Point O is obtained by rotating point G by angle 5pi/12 about point J. Let Q be the midpoint of segment CN. Point R is the reflection of point Q across segment JO. Find the distance between points R and O. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.81", "dataset": "MATH"}
{"messages": [{"content": "Let RS = 12. Let F be the midpoint of segment SR. Point A is the midpoint of segment SF. Line Y is the perpendicular bisector of segment SA. Let O be the line through point A perpendicular to segment SF. Line X is the reflection of line Y across line O. Line X and segment SF intersect at point N. Find the distance between points R and N. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.5", "dataset": "MATH"}
{"messages": [{"content": "HB = 11. Point Q is the reflection of point B across point H. Let L be the midpoint of segment BH. Point T is obtained by rotating point H by angle 2pi/3 about point Q. Let E be the line through points T and Q. Line V is the perpendicular bisector of segment BH. Line I is the reflection of line E across line V. Line O is the reflection of line E across line I. Point K is the reflection of point H across line O. What is the length of segment KL? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57.42", "dataset": "MATH"}
{"messages": [{"content": "FU = 5. Point W is the reflection of point F across point U. Point H is obtained by rotating point W by angle pi/4 about point U. Let J be the midpoint of segment WH. Point Q is the reflection of point H across segment UF. Line Y is the perpendicular bisector of segment UF. Let O be the reflection of point H across point W. Point C is the midpoint of segment QH. Let A be the rotation of point U by angle 11pi/12 around point J. Let L be the midpoint of segment JC. Line N is the reflection of line Y across point A. Line G passes through point L parallel to segment UF. Point B is the intersection of lines N and G. What is the distance between points O and B? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.42", "dataset": "MATH"}
{"messages": [{"content": "Let JY = 9. Let V be the perpendicular bisector of segment YJ. Let D be the midpoint of segment YJ. Let Z be the reflection of point Y across point J. Point U is on line V with |UJ| = 12. Line P is the perpendicular bisector of segment YZ. Let H be the line through point Z parallel to line P. Point G is the midpoint of segment DU. Point C is the reflection of point G across line H. Point O is the reflection of point Z across point U. Find the length of segment CO. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44.32", "dataset": "MATH"}
{"messages": [{"content": "IP = 6. Let Q be the midpoint of segment IP. Let D be the reflection of point I across point P. Point M is the reflection of point Q across point D. Let X be the midpoint of segment QI. Find the length of segment MX. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.5", "dataset": "MATH"}
{"messages": [{"content": "Let PM = 6. Let U be the rotation of point P by angle pi/2 around point M. Let T be the angle bisector of angle UMP. Let Q be the midpoint of segment UP. Let B be the midpoint of segment MU. Let I be the line through point B perpendicular to line T. Point L is the reflection of point U across line I. What is the distance between points L and Q? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.0", "dataset": "MATH"}
{"messages": [{"content": "JO = 2. Let K be the rotation of point O by angle pi/4 around point J. Let V be the line through points J and O. Point Q is the midpoint of segment OJ. Line M is the angle bisector of angle JKQ. Let Z be the reflection of line V across line M. Point A is the reflection of point K across line Z. Point U is the reflection of point O across segment QA. Point H is the intersection of line Z and segment QA. Point N is the reflection of point U across point H. What is the length of segment QN? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.86", "dataset": "MATH"}
{"messages": [{"content": "MS = 8. Let K be the rotation of point S by angle 5pi/6 around point M. Let N be the rotation of point K by angle pi/3 around point M. Let W be the midpoint of segment SN. Point B is obtained by rotating point W by angle pi about point K. Point U is the reflection of point M across point N. Line X passes through points B and S. Line J passes through points W and U. Line L is the angle bisector of angle WNB. Let O be the line through point U parallel to line L. Line F is the reflection of line X across line J. Point Z is the intersection of lines X and O. Point A is the reflection of point K across line O. Let T be the midpoint of segment SZ. Let E be the line through point K parallel to line F. Point D is the reflection of point A across line F. Point I is the reflection of point D across segment MT. Point G is the midpoint of segment BI. Point V is the intersection of segment BN and line E. What is the distance between points V and G? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.9", "dataset": "MATH"}
{"messages": [{"content": "WD = 12. Let N be the reflection of point W across point D. Let V be the midpoint of segment DN. Point F is obtained by rotating point N by angle 7pi/12 about point W. Line Z passes through points F and W. Point R is the reflection of point D across line Z. Point J is the midpoint of segment VD. Let K be the reflection of point F across point J. Find the distance between points K and R. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49.67", "dataset": "MATH"}
{"messages": [{"content": "SL = 5. Point N is obtained by rotating point L by angle 7pi/12 about point S. Let T be the rotation of point S by angle pi/4 around point N. Point H is the midpoint of segment NL. Let C be the reflection of point H across point N. Let U be the line through point C parallel to segment NT. Point M is the reflection of point N across line U. What is the distance between points M and C? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.97", "dataset": "MATH"}
{"messages": [{"content": "AY = 1. Let N be the perpendicular bisector of segment YA. Let H be the reflection of line N through point Y. Let U be the rotation of point A by angle 7pi/12 around point Y. Point Q is the reflection of point Y across line H. Let L be the midpoint of segment YQ. Point M is the midpoint of segment YL. Point G is obtained by rotating point Q by angle 7pi/12 about point U. Let J be the perpendicular bisector of segment GM. Let O be the reflection of line J through point Y. Point I is the midpoint of segment GU. Point R is the reflection of point L across line O. Find the distance between points R and I. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.95", "dataset": "MATH"}
{"messages": [{"content": "BN = 4. Let J be the line through points B and N. Point Y is obtained by rotating point B by angle 7pi/12 about point N. Point A is the midpoint of segment NB. Let X be the rotation of point A by angle 11pi/12 around point Y. Point K is the midpoint of segment AX. Point D is the reflection of point K across line J. Line V is the perpendicular bisector of segment KA. Point M is the reflection of point D across line V. Find the length of segment MY. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.32", "dataset": "MATH"}
{"messages": [{"content": "Let TC = 5. Let H be the midpoint of segment TC. Let TN = 1. Line I is the angle bisector of angle HTN. Let O be the reflection of line I through point H. Point W is on segment NT. Line X passes through point W perpendicular to segment NT. Line J is the reflection of line X across line I. Line S is the reflection of line J across line O. Point Q is the midpoint of segment NT. Point D lies on line S. Let Z be the midpoint of segment DQ. Let A be the midpoint of segment TD. What is the length of segment ZA? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
{"messages": [{"content": "Let HR = 1. Let Q be the reflection of point H across point R. Let W be the rotation of point Q by angle pi/12 around point R. Let Z be the rotation of point W by angle pi around point Q. Line T is the perpendicular bisector of segment ZQ. Line K passes through point H parallel to line T. Let X be the angle bisector of angle ZHW. Let U be the rotation of point Q by angle 5pi/6 around point R. Point V is the reflection of point U across line X. Let F be the reflection of line X through point R. Point P is the intersection of lines F and K. Let S be the midpoint of segment HP. What is the length of segment VS? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.52", "dataset": "MATH"}
{"messages": [{"content": "KM = 4. Let Y be the midpoint of segment KM. Line Z is the perpendicular bisector of segment YM. Point E is the reflection of point K across line Z. Let F be the rotation of point K by angle 3pi/4 around point E. Line H is the angle bisector of angle FMK. Point Q is the reflection of point Y across line H. Line C is the perpendicular bisector of segment QF. Point P is the reflection of point M across line C. Find the length of segment PY. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.26", "dataset": "MATH"}
{"messages": [{"content": "Let HR = 11. Let S be the reflection of point H across point R. Let V be the rotation of point H by angle 3pi/4 around point R. Let J be the rotation of point R by angle pi/2 around point V. Let U be the reflection of point S across point J. Point W is obtained by rotating point S by angle 2pi/3 about point J. Let K be the rotation of point H by angle pi/4 around point U. Line G is the angle bisector of angle HVW. Point F is the midpoint of segment WK. Line Y is the reflection of line G across point F. Line Z passes through point V perpendicular to line G. Let I be the reflection of line Z through point S. Point D is the intersection of lines I and Y. Find the distance between points K and D. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46.35", "dataset": "MATH"}
{"messages": [{"content": "DA = 3. Let O be the midpoint of segment DA. Point M is the midpoint of segment AO. Let L be the midpoint of segment MO. Let Q be the midpoint of segment LD. Let W be the reflection of point D across point L. Let G be the midpoint of segment DQ. Line T is the perpendicular bisector of segment LD. Line P passes through point O perpendicular to segment LD. Point I is the midpoint of segment QG. Line Z passes through point W parallel to line T. Let E be the line through point M parallel to line Z. Point F is the reflection of point W across line P. Point N is the reflection of point F across line E. Let Y be the midpoint of segment NL. Find the distance between points I and Y. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.86", "dataset": "MATH"}
{"messages": [{"content": "Let RQ = 5. Point G is obtained by rotating point Q by angle pi/2 about point R. Point W is the reflection of point G across point R. Let O be the rotation of point G by angle 7pi/12 around point Q. Point J is the reflection of point W across point O. Point Z is the midpoint of segment OJ. Line S is the perpendicular bisector of segment OJ. Line H is the angle bisector of angle JZG. Line B is the reflection of line H across line S. Point X is the intersection of segment RJ and line B. Find the distance between points W and X. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "ME = 10. Let T be the rotation of point E by angle pi/12 around point M. Point Y is the midpoint of segment ET. Line J is the perpendicular bisector of segment YT. Line Q is the reflection of line J across point Y. Point S is the reflection of point M across line Q. What is the distance between points S and M? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.31", "dataset": "MATH"}
{"messages": [{"content": "QK = 11. Point Y is the midpoint of segment KQ. Point A is the reflection of point Q across point K. Let W be the rotation of point K by angle pi/4 around point Y. Point V is the midpoint of segment YA. Point P is the midpoint of segment WA. Point N is the reflection of point Y across point Q. Point D is the reflection of point V across point N. What is the distance between points P and D? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40.49", "dataset": "MATH"}
{"messages": [{"content": "YB = 2. Let H be the midpoint of segment BY. Let W be the perpendicular bisector of segment YB. Line Q is the reflection of line W across point B. Let S be the reflection of point H across point B. Let U be the line through point B perpendicular to line Q. Point F is obtained by rotating point S by angle pi/12 about point B. Let G be the reflection of point Y across point F. Let E be the reflection of line U through point G. Line O is the reflection of line E across line U. Point T is the reflection of point S across point H. Point C is the reflection of point H across line O. Find the length of segment TC. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.88", "dataset": "MATH"}
{"messages": [{"content": "VO = 6. Let X be the vector from point O to point V. Point B is the translation of point V by vector X. Point Q is obtained by rotating point V by angle 3pi/4 about point O. Let R be the rotation of point O by angle pi/3 around point Q. Let M be the angle bisector of angle QRO. Line S passes through points O and B. Point T is the reflection of point R across point O. Point L is the midpoint of segment VB. Line K is the reflection of line M across line S. Point U is obtained by rotating point T by angle pi/2 about point V. Let D be the rotation of point Q by angle 2pi/3 around point U. Let W be the line through points L and D. Let H be the midpoint of segment VT. Point G is the midpoint of segment HV. Point P is the intersection of lines W and K. Find the length of segment GP. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.16", "dataset": "MATH"}
{"messages": [{"content": "JW = 1. Point F is obtained by rotating point J by angle pi/3 about point W. Line Y passes through points W and F. Point I is the reflection of point J across line Y. Point B is the reflection of point J across point F. Let Z be the midpoint of segment BI. What is the length of segment ZB? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "UM = 4. Let D be the rotation of point M by angle pi/3 around point U. Line S passes through points M and D. Let L be the midpoint of segment UD. Let C be the midpoint of segment LM. Let E be the midpoint of segment LD. Point V is the reflection of point C across line S. Point J is the midpoint of segment DM. Point Q is the reflection of point J across segment CE. Let I be the rotation of point L by angle 11pi/12 around point V. Point B is obtained by rotating point E by angle 5pi/12 about point V. Let H be the angle bisector of angle JQI. Point F is the reflection of point B across line H. Point Z is the reflection of point J across segment LD. Let Y be the midpoint of segment ZU. What is the distance between points F and Y? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.87", "dataset": "MATH"}
{"messages": [{"content": "Let XN = 4. Let R be the vector from point N to point X. Let O be the rotation of point X by angle 7pi/12 around point N. Point E is the translation of point X by vector R. Let S be the reflection of point X across point E. Point J is obtained by rotating point O by angle pi/3 about point E. Let B be the midpoint of segment XE. Let V be the reflection of point J across point E. Let C be the perpendicular bisector of segment SO. Let Y be the reflection of line C through point V. Point H is the reflection of point X across line Y. Point D is the midpoint of segment OE. Point U is the reflection of point E across line C. Let Z be the reflection of point D across point B. Point A is the midpoint of segment JX. Point T is the reflection of point A across segment HE. Let L be the midpoint of segment ZU. Find the length of segment LT. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.06", "dataset": "MATH"}
{"messages": [{"content": "PI = 1. Point V is obtained by rotating point I by angle pi/12 about point P. Let A be the midpoint of segment PV. Let F be the angle bisector of angle IAP. Point T is the reflection of point V across point P. Point C is the midpoint of segment PI. Let X be the line through point P parallel to line F. Let M be the perpendicular bisector of segment CV. Point N is the midpoint of segment PA. Let O be the line through point N parallel to line M. Lines O and X intersect at point S. Point R is the midpoint of segment SV. What is the length of segment TR? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.58", "dataset": "MATH"}
{"messages": [{"content": "QJ = 5. Point M is obtained by rotating point J by angle 11pi/12 about point Q. Let H be the reflection of point M across point Q. Point N is the midpoint of segment QH. Point P is the reflection of point N across segment JQ. Find the length of segment PH. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Let UC = 11. Let T be the rotation of point U by angle 11pi/12 around point C. Let G be the rotation of point U by angle pi/3 around point T. Point V is the midpoint of segment TG. Point F is the midpoint of segment UV. Let L be the midpoint of segment FU. Line Q is the angle bisector of angle VGC. Line Y passes through point V perpendicular to line Q. Let N be the perpendicular bisector of segment LF. Let A be the perpendicular bisector of segment UF. Let M be the reflection of point T across point G. Line B is the reflection of line Y across line N. Line B and segment TG intersect at point J. Point Z is the reflection of point J across point M. Point E is the reflection of point M across line A. What is the length of segment EZ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38.72", "dataset": "MATH"}
{"messages": [{"content": "ID = 3. Let G be the reflection of point I across point D. Line P is the angle bisector of angle GDI. Line Z passes through point D perpendicular to line P. Point Y lies on line P at distance 5 from point D. Let B be the rotation of point D by angle pi/12 around point Y. Line K is the reflection of line Z across point B. Point M is the reflection of point G across line K. Point L is the midpoint of segment GM. What is the length of segment LI? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.01", "dataset": "MATH"}
{"messages": [{"content": "Let AW = 10. Let D be the line through points A and W. Point F is the reflection of point W across point A. Let K be the vector from point W to point A. Line N passes through point W perpendicular to line D. Let M be the midpoint of segment FA. Point P is the translation of point M by vector K. Point B is obtained by rotating point F by angle 11pi/12 about point W. Point Q is the reflection of point P across line N. Let Y be the midpoint of segment MW. Point X is the reflection of point Q across segment MB. Find the length of segment YX. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32.91", "dataset": "MATH"}
{"messages": [{"content": "Let YX = 4. Let YL = 2. Let V be the perpendicular bisector of segment LY. Point Z is the reflection of point L across point X. Point E is on line V with |EZ| = 2. Point M is obtained by rotating point E by angle pi/2 about point X. Let G be the midpoint of segment MX. Point N is the reflection of point L across point Y. Point A is the reflection of point L across segment MG. Point H is the reflection of point N across segment MG. What is the distance between points A and H? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Let KA = 11. Line O passes through points K and A. Point Y is the reflection of point A across point K. Point G is obtained by rotating point A by angle pi/3 about point Y. Line V passes through point G parallel to line O. Point H is the reflection of point K across point A. Point F is the reflection of point K across line V. Let M be the reflection of line O through point F. Point N is the reflection of point F across point A. Point X is the midpoint of segment FH. Point U is the reflection of point X across line M. What is the distance between points U and N? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "171.83", "dataset": "MATH"}
{"messages": [{"content": "DK = 8. Let S be the reflection of point K across point D. Let Q be the reflection of point D across point K. Let L be the rotation of point Q by angle 11pi/12 around point K. Line B is the perpendicular bisector of segment LD. Line T passes through point L parallel to line B. Let Y be the midpoint of segment LD. Point C is the reflection of point S across line T. Point G is the midpoint of segment YC. Find the distance between points Y and G. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.48", "dataset": "MATH"}
{"messages": [{"content": "DI = 12. Point T is obtained by rotating point I by angle 7pi/12 about point D. Let F be the vector from point D to point T. Let Y be the midpoint of segment ID. Let X be the line through point I parallel to segment YT. Let C be the reflection of line X through point T. Line P passes through points T and D. Let J be point I translated by vector F. Point S is the reflection of point J across line P. Line N is the angle bisector of angle SJD. Let E be the line through point T parallel to line N. Let K be the reflection of line E across line C. Point M is the intersection of lines X and K. Find the distance between points M and J. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.72", "dataset": "MATH"}
{"messages": [{"content": "Let GN = 2. Let T be the reflection of point G across point N. Point Y is the reflection of point N across point T. Point U is obtained by rotating point T by angle pi/3 about point G. Let A be the angle bisector of angle UNT. Line E is the perpendicular bisector of segment NU. Line P is the angle bisector of angle GYU. Line O passes through point U parallel to line E. Let C be the line through point G perpendicular to line P. Line S is the reflection of line C across line A. Point X is the reflection of point N across line C. Point H is the reflection of point U across point N. Point L is the reflection of point X across line S. Point D is the reflection of point H across line O. Point I is the reflection of point T across point L. What is the distance between points D and I? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.18", "dataset": "MATH"}
{"messages": [{"content": "CO = 9. Point S is the midpoint of segment CO. Let M be the rotation of point S by angle 2pi/3 around point C. Point H is the midpoint of segment OS. Let T be the vector from point C to point H. Point W is the translation of point H by vector T. Let L be point M translated by vector T. Point V is obtained by rotating point M by angle 5pi/12 about point L. Point B is the midpoint of segment WV. Let U be the midpoint of segment BC. Point Z is the midpoint of segment VU. What is the distance between points Z and W? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.22", "dataset": "MATH"}
{"messages": [{"content": "EM = 12. Point D is the midpoint of segment ME. Line C is the perpendicular bisector of segment ME. Point J is on line C with |JD| = 6. Point S is the reflection of point J across segment ME. Let G be the midpoint of segment ED. Point A is the midpoint of segment SE. What is the measure of angle EAG, in radians? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.79", "dataset": "MATH"}
{"messages": [{"content": "XR = 6. Point F is obtained by rotating point X by angle 5pi/12 about point R. Point U is obtained by rotating point F by angle pi/12 about point R. Point L is the midpoint of segment RU. Point K is the reflection of point L across segment UF. Let T be the midpoint of segment XK. What is the length of segment FT? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.28", "dataset": "MATH"}
{"messages": [{"content": "JZ = 9. Let T be the reflection of point J across point Z. Let K be the perpendicular bisector of segment JT. Point A is the midpoint of segment ZJ. Point Y is obtained by rotating point A by angle pi/2 about point T. Let E be the perpendicular bisector of segment JA. Let M be the reflection of line K across line E. Let V be the line through point Y parallel to segment ZJ. Let R be the reflection of line E across line M. Point S is the intersection of lines R and V. What is the distance between points S and T? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32.22", "dataset": "MATH"}
{"messages": [{"content": "AM = 12. Point P is the reflection of point A across point M. Point I is obtained by rotating point P by angle pi/4 about point M. Let G be the perpendicular bisector of segment PM. Let F be the line through point P perpendicular to line G. Let T be the rotation of point I by angle pi/12 around point A. Point H is the midpoint of segment MI. Point L is the reflection of point H across line F. Let K be the reflection of point L across point T. Point C is the reflection of point K across segment MT. Find the distance between points H and C. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26.18", "dataset": "MATH"}
{"messages": [{"content": "RB = 2. Let X be the vector from point R to point B. Let E be the rotation of point B by angle pi/3 around point R. Point T is the reflection of point E across point R. Let Q be the line through points B and T. Point A is the translation of point T by vector X. Let P be the rotation of point T by angle pi/12 around point R. Line D is the reflection of line Q across point A. Point C is the reflection of point E across line D. Point M is the midpoint of segment CB. Point Z is the midpoint of segment PC. What is the distance between points Z and M? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.59", "dataset": "MATH"}
{"messages": [{"content": "Let AS = 8. Let L be the reflection of point A across point S. Let Z be the vector from point A to point L. Point C is the midpoint of segment LS. Point X is obtained by rotating point A by angle 11pi/12 about point L. Let B be the perpendicular bisector of segment LX. Let D be the rotation of point S by angle pi/3 around point C. Point J is the reflection of point D across segment SL. Let P be the reflection of point A across point L. Point R is the translation of point P by vector Z. Point U is the translation of point R by vector Z. Let T be the midpoint of segment JL. Let H be point U translated by vector Z. Let G be the midpoint of segment DH. Point O is the reflection of point G across line B. Let I be the midpoint of segment AT. Point N is the midpoint of segment OC. What is the distance between points I and N? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.21", "dataset": "MATH"}
{"messages": [{"content": "NF = 9. S is placed 6 units away from F. Let NW = 1. Point B is the midpoint of segment SF. Point M is the reflection of point B across segment WS. Point K is the reflection of point F across segment WS. Find the distance between points M and K. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Let VC = 1. Let Z be the vector from point V to point C. Point R is obtained by rotating point V by angle 5pi/12 about point C. Let Y be the vector from point R to point C. Point G is obtained by rotating point C by angle pi/12 about point R. Point D is the translation of point G by vector Y. Point W is the reflection of point V across segment GR. Point X is the intersection of segments VC and GR. Let P be point D translated by vector Z. Point A is the reflection of point P across segment VC. Point J is the reflection of point C across segment GR. Line O is the perpendicular bisector of segment PW. Let K be the reflection of line O through point X. Let L be the midpoint of segment RJ. Point S is the midpoint of segment LD. Point T is the reflection of point A across line K. Find the distance between points T and S. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
{"messages": [{"content": "FS = 9. Point L is obtained by rotating point F by angle 5pi/6 about point S. Point T is the reflection of point F across point L. Let K be the reflection of point L across point S. Let O be the reflection of point K across point T. Point I is the midpoint of segment SL. Let G be the midpoint of segment TI. Let X be the midpoint of segment TG. Let P be the midpoint of segment FO. Point J is the midpoint of segment PX. What is the length of segment PJ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.02", "dataset": "MATH"}
{"messages": [{"content": "EW = 3. Let Q be the perpendicular bisector of segment EW. Let B be the rotation of point E by angle pi/4 around point W. Point G is the midpoint of segment BW. Point D is the midpoint of segment EB. Let H be the line through point E perpendicular to line Q. Let A be the midpoint of segment ED. Let X be the line through point W parallel to line Q. Let R be the reflection of point B across point A. Let U be the rotation of point R by angle 11pi/12 around point E. Let F be the line through point D perpendicular to line H. Let I be the line through points B and A. Line Z passes through points D and G. Line M is the reflection of line I across line X. Let L be the reflection of line X across line F. Point P is the reflection of point U across line L. Lines Z and M intersect at point J. What is the distance between points J and P? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.95", "dataset": "MATH"}
{"messages": [{"content": "FM = 9. Point D is obtained by rotating point F by angle 2pi/3 about point M. Point E is obtained by rotating point F by angle pi/4 about point M. Let K be the rotation of point D by angle 5pi/6 around point F. Let I be the vector from point D to point F. Let O be point M translated by vector I. Line V is the angle bisector of angle EOF. Point B is the reflection of point F across line V. Let A be the line through points F and M. Line Q passes through point O perpendicular to line A. Line G passes through points B and F. Let R be point B translated by vector I. Let C be the midpoint of segment FK. Let H be the reflection of line Q across line G. Point W is the reflection of point R across segment FK. Let U be the midpoint of segment WR. Point J is the intersection of lines A and H. Point P is the midpoint of segment JC. What is the length of segment UP? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.36", "dataset": "MATH"}
{"messages": [{"content": "Let JF = 6. Point Q is the reflection of point F across point J. Let P be the angle bisector of angle FQJ. Let W be the line through point F perpendicular to line P. JC = 9. Line L is the perpendicular bisector of segment QJ. Point Y lies on line L at distance 12 from point Q. Point N is the reflection of point J across line W. Let T be the midpoint of segment YJ. Point D lies on segment CN. Point A is the reflection of point T across line W. Point I is the midpoint of segment DT. Point G is the reflection of point A across point I. Find the length of segment DG. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.0", "dataset": "MATH"}
{"messages": [{"content": "WR = 2. Point H is the reflection of point R across point W. Let X be the midpoint of segment RW. Let F be the perpendicular bisector of segment HX. Point K is the reflection of point X across point H. Point D is the reflection of point H across point K. Point T is the reflection of point K across line F. Point O is the midpoint of segment DW. Point G is on line F with |GT| = 2. Point V is obtained by rotating point D by angle pi about point G. Line M is the perpendicular bisector of segment VG. Let N be the midpoint of segment VR. Line S is the reflection of line M across point O. Point B is the reflection of point K across point N. Point U is the reflection of point B across line S. Let L be the reflection of point O across point G. What is the length of segment UL? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41.87", "dataset": "MATH"}
{"messages": [{"content": "Let SC = 6. Let I be the rotation of point S by angle pi/6 around point C. Let O be the line through point C perpendicular to segment CS. Point F is the reflection of point I across line O. Point B is the midpoint of segment CS. Point N is the midpoint of segment BI. Let G be the midpoint of segment NF. Let L be the midpoint of segment FI. What is the distance between points L and G? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.93", "dataset": "MATH"}
{"messages": [{"content": "Let OM = 9. Point E is the reflection of point M across point O. Line B passes through points O and E. Point I is the reflection of point O across point M. Let D be the rotation of point I by angle 5pi/12 around point O. Let Q be the midpoint of segment MD. Let J be the midpoint of segment IQ. Point U is the reflection of point J across line B. Let G be the reflection of point M across point U. Find the length of segment QG. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.58", "dataset": "MATH"}
{"messages": [{"content": "RV = 1. Point F is the midpoint of segment VR. Point K is the reflection of point F across point V. Let H be the rotation of point K by angle 5pi/6 around point V. Point W is the reflection of point R across segment KH. Point Y is the reflection of point R across segment HW. Point Q is the reflection of point V across segment KH. What is the length of segment YQ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.47", "dataset": "MATH"}
{"messages": [{"content": "Let MB = 7. Line T passes through points M and B. Point P is the midpoint of segment BM. Let Z be the reflection of point P across point M. Line X passes through point Z perpendicular to line T. Let N be the rotation of point Z by angle 2pi/3 around point B. Point Q is the reflection of point M across line X. Point S is obtained by rotating point N by angle 11pi/12 about point Q. Point G is the reflection of point P across line X. Point I is the reflection of point B across point N. Point V is the midpoint of segment GS. Let E be the reflection of point N across point V. Find the distance between points E and I. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75.6", "dataset": "MATH"}
{"messages": [{"content": "UE = 11. Point A is obtained by rotating point E by angle 7pi/12 about point U. Point L is obtained by rotating point E by angle 2pi/3 about point U. Point H is the midpoint of segment LA. Let T be the midpoint of segment HE. Let D be the midpoint of segment HA. Find the distance between points D and T. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.73", "dataset": "MATH"}
{"messages": [{"content": "Let JL = 3. JN = 5. Line K is the perpendicular bisector of segment LN. Point O is the reflection of point J across line K. Let V be the midpoint of segment JN. Point T is the reflection of point V across line K. Point W is the reflection of point O across point L. What is the length of segment TW? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.5", "dataset": "MATH"}
{"messages": [{"content": "RY = 5. Let K be the midpoint of segment YR. Let F be the angle bisector of angle YKR. Point O is the midpoint of segment RK. Let S be the line through point R parallel to line F. Let I be the reflection of line F across line S. Point Q is the reflection of point R across line I. Find the distance between points Q and O. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.25", "dataset": "MATH"}
{"messages": [{"content": "PD = 12. Let Q be the perpendicular bisector of segment DP. Point L is obtained by rotating point P by angle 5pi/12 about point D. Line O is the angle bisector of angle PLD. Point B is the reflection of point L across line Q. Let N be the midpoint of segment LD. Point K is the reflection of point N across line O. Find the length of segment BK. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.22", "dataset": "MATH"}
{"messages": [{"content": "Let TF = 12. Let W be the reflection of point F across point T. Let S be the line through points T and F. Line X passes through point W perpendicular to line S. Point I is on line X with |IT| = 8. Let C be the reflection of point W across point F. Let A be the midpoint of segment IT. Point L is the midpoint of segment TC. Point J is the midpoint of segment LF. Let R be the midpoint of segment JF. What is the length of segment RA? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.91", "dataset": "MATH"}
{"messages": [{"content": "GJ = 2. Line V passes through points J and G. Let X be the reflection of point G across point J. Line N is the perpendicular bisector of segment JG. Point E lies on line V. Point Q is the reflection of point E across point G. Point F is on line N with |FX| = 11. Let A be the angle bisector of angle QJF. Let I be the perpendicular bisector of segment XJ. Point W is the reflection of point F across line I. Point Z is the reflection of point W across line A. Point C is the reflection of point G across point F. Let H be the midpoint of segment ZC. What is the distance between points H and Z? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.05", "dataset": "MATH"}
{"messages": [{"content": "Let IF = 7. Let J be the rotation of point F by angle 11pi/12 around point I. Line T passes through point F perpendicular to segment IF. Let X be the line through point I parallel to line T. Point U is obtained by rotating point J by angle 7pi/12 about point F. Point G is the reflection of point U across line T. Point W is on line X. Point V is the midpoint of segment WU. Line O passes through point V perpendicular to line X. Point Y is the intersection of segments IG and JU. Let B be the midpoint of segment YF. Point S is the reflection of point W across line O. Find the length of segment SB. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.99", "dataset": "MATH"}
{"messages": [{"content": "Let JS = 9. Let K be the reflection of point J across point S. Let Z be the rotation of point K by angle 3pi/4 around point S. Let Y be the reflection of point K across point Z. Let N be the angle bisector of angle SKY. Let V be the reflection of line N through point S. Point O is the reflection of point Z across line V. Find the distance between points O and Z. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.51", "dataset": "MATH"}
{"messages": [{"content": "Let DO = 7. Point J is obtained by rotating point D by angle pi/3 about point O. Point L lies on segment OJ. Line P is the angle bisector of angle DOL. Let X be the reflection of line P through point J. Line T passes through point D parallel to segment OJ. Lines X and T intersect at point A. Let S be the reflection of point O across point A. What is the distance between points S and A? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25.24", "dataset": "MATH"}
{"messages": [{"content": "Let VG = 6. Let F be the rotation of point G by angle pi/2 around point V. Point A is obtained by rotating point G by angle 7pi/12 about point F. Let S be the midpoint of segment FV. Point T is the midpoint of segment AF. Let H be the midpoint of segment TS. Point E is the reflection of point H across point G. Point Y is the reflection of point E across segment FV. Find the length of segment EY. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.88", "dataset": "MATH"}
{"messages": [{"content": "OM = 10. Point Q is the reflection of point M across point O. Let U be the perpendicular bisector of segment MO. Point P is the reflection of point Q across line U. Let Z be the perpendicular bisector of segment PM. Point S is the reflection of point O across line Z. Find the distance between points P and S. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.0", "dataset": "MATH"}
{"messages": [{"content": "UB = 7. Let M be the rotation of point B by angle pi/12 around point U. Point V is the reflection of point M across point U. Point D is the reflection of point B across segment UM. Let R be the midpoint of segment VU. Let T be the reflection of point R across point D. Let F be the perpendicular bisector of segment UM. Point E is the reflection of point V across line F. Let P be the line through point B perpendicular to line F. Point H is the reflection of point E across line P. What is the distance between points T and H? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.85", "dataset": "MATH"}
{"messages": [{"content": "Let UC = 1. Point L is obtained by rotating point C by angle 2pi/3 about point U. Let T be the midpoint of segment UL. Let N be the rotation of point L by angle pi/4 around point T. Let I be the perpendicular bisector of segment TC. Point H lies on line I. Point A is the reflection of point U across segment HN. What is the length of segment NA? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.92", "dataset": "MATH"}
{"messages": [{"content": "Let FH = 3. Line W is the perpendicular bisector of segment FH. Let U be the midpoint of segment HF. Point X is on line W with |XU| = 2. Let P be the midpoint of segment HU. Let G be the angle bisector of angle FUX. Point I is the reflection of point X across line G. Line O passes through point P perpendicular to line G. Point M is the reflection of point I across line O. Let D be the reflection of point M across point H. What is the length of segment MD? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.7", "dataset": "MATH"}
{"messages": [{"content": "ZW = 2. Let C be the rotation of point W by angle pi/6 around point Z. Point T is the midpoint of segment CZ. Point D is the reflection of point T across segment CW. Let F be the line through point Z parallel to segment CW. Point X is obtained by rotating point Z by angle pi/12 about point T. Let H be the rotation of point X by angle pi around point C. Line S passes through points W and H. Point M is the midpoint of segment CW. Point U is the reflection of point X across line F. Point R is the midpoint of segment TH. Line E passes through points U and R. Line G is the reflection of line E across point M. Point J is the reflection of point U across line S. Line K passes through point D perpendicular to line G. Point Y is the reflection of point W across line K. What is the length of segment JY? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.53", "dataset": "MATH"}
{"messages": [{"content": "JP = 12. Let V be the rotation of point P by angle pi/3 around point J. Point D is the midpoint of segment JP. Point K is the midpoint of segment VP. Let A be the rotation of point D by angle 5pi/12 around point V. Point U is the midpoint of segment KJ. Let B be the reflection of point U across point A. Let G be the perpendicular bisector of segment UB. Let M be the line through point P parallel to line G. Point H is the reflection of point D across line M. Let E be the reflection of point V across point U. Line O passes through points A and E. Let T be the reflection of point K across point H. Point Q is the reflection of point J across line O. Find the length of segment TQ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.1", "dataset": "MATH"}
{"messages": [{"content": "OC = 11. Point P is the reflection of point O across point C. Line J passes through point O perpendicular to segment PO. Point U is the midpoint of segment CO. Let H be the reflection of point P across point O. Let B be the perpendicular bisector of segment PO. Let I be the reflection of point H across point C. Let A be the rotation of point O by angle pi/6 around point I. Let V be the midpoint of segment CA. Let T be the line through point V parallel to line B. Point E is the reflection of point V across line J. Point F is obtained by rotating point V by angle pi/2 about point E. Let Y be the reflection of point F across point H. Point W is the reflection of point A across segment PO. Let X be the line through point U parallel to segment YW. Segment PO and line T intersect at point K. Line L passes through point F parallel to segment YW. Let D be the reflection of line B across line L. Line R is the reflection of line D across point H. Point M is the intersection of lines X and R. Find the distance between points M and K. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51.13", "dataset": "MATH"}
{"messages": [{"content": "Let LK = 2. Line W is the perpendicular bisector of segment LK. Point P is obtained by rotating point K by angle 11pi/12 about point L. Line D is the perpendicular bisector of segment LP. Let Z be the reflection of line W through point K. Let X be the reflection of line Z across line W. Let Y be the reflection of line W across line D. Point S is the intersection of lines Z and Y. Let I be the line through points K and S. Lines X and I intersect at point N. What is the distance between points S and N? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44.42", "dataset": "MATH"}
{"messages": [{"content": "SB = 1. Let X be the midpoint of segment SB. Point D is the midpoint of segment BX. Let I be the midpoint of segment BD. Let O be the rotation of point S by angle pi/6 around point X. Line G passes through points X and D. Line T passes through points B and O. Let Q be the reflection of line G across line T. Point U is the reflection of point I across line Q. What is the length of segment UO? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.88", "dataset": "MATH"}
{"messages": [{"content": "Let NM = 12. Point F is obtained by rotating point M by angle pi/2 about point N. Let W be the vector from point N to point M. Let J be the perpendicular bisector of segment NM. Let X be the line through point N perpendicular to line J. Point P is the reflection of point F across line X. Let D be point P translated by vector W. Line O is the perpendicular bisector of segment MF. Point Q is the reflection of point D across line O. Let K be the midpoint of segment PN. Point R is the reflection of point K across point Q. Point L is the midpoint of segment QR. Find the length of segment LR. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.82", "dataset": "MATH"}
{"messages": [{"content": "Let IG = 6. Let U be the midpoint of segment GI. Let B be the rotation of point G by angle pi/3 around point I. Let M be the vector from point G to point B. Let D be the line through points I and U. Point O is the midpoint of segment GB. Let H be point O translated by vector M. Point K is the reflection of point B across line D. Let V be the rotation of point K by angle pi/2 around point B. Point X is the reflection of point U across segment HB. Point W is the midpoint of segment XV. Let Y be the midpoint of segment WG. Let N be the reflection of point Y across point U. Find the length of segment NV. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.17", "dataset": "MATH"}
{"messages": [{"content": "Let BX = 6. Let I be the reflection of point B across point X. Let J be the rotation of point I by angle 2pi/3 around point B. Point D is the reflection of point J across segment BX. Let C be the line through points D and I. Point Q is the reflection of point B across line C. Let Z be the midpoint of segment QX. Point O is the midpoint of segment BD. Point V is the reflection of point Z across segment BD. What is the distance between points V and O? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.0", "dataset": "MATH"}
{"messages": [{"content": "Let VH = 5. Let X be the rotation of point H by angle 5pi/12 around point V. Let L be the reflection of point H across point V. Let R be the line through points X and V. Point Y is the reflection of point X across segment HV. Let D be the perpendicular bisector of segment LX. Let A be the reflection of line D across line R. Line B passes through point X parallel to line A. Let Q be the reflection of line R across line A. Point S is the intersection of lines B and Q. Line P passes through point Y perpendicular to segment HV. Point C is the reflection of point S across segment HV. Point Z is the reflection of point C across line P. What is the distance between points V and Z? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.36", "dataset": "MATH"}
{"messages": [{"content": "Let ZD = 3. Let S be the rotation of point D by angle 11pi/12 around point Z. Let F be the angle bisector of angle ZDS. Point M is the reflection of point D across point S. Point E is the reflection of point M across point D. Point H is the reflection of point S across line F. Point K is the reflection of point E across segment HS. Find the length of segment KH. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.81", "dataset": "MATH"}
{"messages": [{"content": "Let EF = 6. Let W be the perpendicular bisector of segment FE. Let I be the midpoint of segment FE. Let G be the rotation of point F by angle 7pi/12 around point I. Point N is the midpoint of segment GE. Point Z is the reflection of point N across point G. Let H be the line through point I parallel to segment GZ. Point J is the reflection of point G across line W. Point C is the reflection of point Z across segment FE. Point R is the reflection of point N across line H. Let A be the midpoint of segment RC. Find the distance between points A and J. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.81", "dataset": "MATH"}
{"messages": [{"content": "ZR = 3. Let I be the rotation of point R by angle pi/4 around point Z. Point K is the reflection of point R across point I. Point G is obtained by rotating point R by angle 5pi/12 about point I. Point A is the midpoint of segment IG. Let D be the rotation of point A by angle pi/4 around point I. Point W is the midpoint of segment DI. Let V be the midpoint of segment KW. Point S is the midpoint of segment GV. Find the distance between points S and V. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
{"messages": [{"content": "Let ZA = 8. Let V be the rotation of point Z by angle 7pi/12 around point A. Let I be the midpoint of segment AV. Line S is the angle bisector of angle AZI. Point X is the reflection of point I across line S. Let N be the reflection of point Z across point V. Point K is the reflection of point A across segment VN. What is the length of segment KX? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.95", "dataset": "MATH"}
{"messages": [{"content": "Let AB = 10. Let E be the perpendicular bisector of segment BA. Point F is obtained by rotating point A by angle pi/4 about point B. Point O lies on line E at distance 3 from point F. Let Q be the reflection of point A across point B. Point L lies on line E at distance 7 from point O. Let W be the reflection of point O across point F. Let N be the midpoint of segment WL. Let J be the perpendicular bisector of segment AN. Point G is the reflection of point Q across line J. Find the distance between points N and G. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.0", "dataset": "MATH"}
{"messages": [{"content": "XZ = 10. Point D is the reflection of point X across point Z. Line E is the angle bisector of angle ZXD. Let P be the rotation of point Z by angle 2pi/3 around point X. Line L passes through point P perpendicular to line E. Point I is the reflection of point D across line L. Let U be the reflection of point X across point I. Let F be the reflection of point X across point U. Let V be the midpoint of segment FP. Find the distance between points V and F. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57.66", "dataset": "MATH"}
{"messages": [{"content": "Let JW = 12. Point N is obtained by rotating point J by angle pi/12 about point W. Let B be the midpoint of segment NJ. Point S is the midpoint of segment WJ. Let D be the reflection of point W across point B. Find the length of segment SD. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.86", "dataset": "MATH"}
{"messages": [{"content": "HK = 8. Let B be the perpendicular bisector of segment HK. Let W be the reflection of point H across point K. Point O lies on line B at distance 6 from point K. Let J be the reflection of point W across point O. Let M be the line through point O perpendicular to line B. Point R is the midpoint of segment JO. Point N is the reflection of point H across line M. Let V be the midpoint of segment NR. Find the distance between points V and R. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Let TZ = 8. Point H is the midpoint of segment TZ. Point M is obtained by rotating point Z by angle 2pi/3 about point H. Let C be the reflection of point M across point H. Let G be the line through points M and Z. Point P is the reflection of point H across line G. Point B is the reflection of point H across point C. What is the distance between points P and B? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.58", "dataset": "MATH"}
{"messages": [{"content": "AB = 2. Point O is obtained by rotating point A by angle pi/12 about point B. Let W be the vector from point B to point O. Let L be the angle bisector of angle BOA. Point M is the translation of point A by vector W. Let I be the line through points M and O. Let R be the reflection of line I across line L. Point T is the midpoint of segment BO. Let J be the line through point T perpendicular to line R. Point P is the reflection of point A across line J. Let Q be the midpoint of segment PA. What is the length of segment OQ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.19", "dataset": "MATH"}
{"messages": [{"content": "EW = 11. Point G is the reflection of point W across point E. Let S be the rotation of point E by angle pi/3 around point W. Let Y be the midpoint of segment GE. Let C be the reflection of point G across point S. Let B be the vector from point E to point C. Point U is the translation of point S by vector B. Line P passes through points Y and S. Let R be the angle bisector of angle UGW. Let K be the reflection of line R across line P. Point I is obtained by rotating point C by angle 5pi/12 about point W. Let D be the perpendicular bisector of segment UW. Point X is the reflection of point I across segment UW. Line Q passes through point X parallel to line D. Lines Q and K intersect at point N. Find the length of segment NG. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.62", "dataset": "MATH"}
{"messages": [{"content": "CB = 1. Line A is the perpendicular bisector of segment BC. Let Q be the line through point C perpendicular to segment BC. Point P lies on line A at distance 8 from point B. Point M is the reflection of point P across segment BC. Point J is the reflection of point P across line Q. Point O is the midpoint of segment PJ. Let W be the perpendicular bisector of segment JO. Point H is the reflection of point M across line W. Let D be the midpoint of segment MB. What is the length of segment DH? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.37", "dataset": "MATH"}
{"messages": [{"content": "OE = 12. Let Q be the midpoint of segment EO. Point N is the reflection of point Q across point E. Point A is the reflection of point E across point N. Let X be the reflection of point A across point Q. What is the distance between points X and A? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36.0", "dataset": "MATH"}
{"messages": [{"content": "CI = 1. Point H is obtained by rotating point I by angle 2pi/3 about point C. Point U is the reflection of point H across point C. Point D is obtained by rotating point C by angle pi/6 about point I. Let R be the reflection of point C across point I. Line N passes through points R and C. Let Z be the midpoint of segment ID. Let E be the line through point Z parallel to line N. Point M is the reflection of point D across line E. Point B is the reflection of point M across segment ID. Let P be the midpoint of segment RB. Find the distance between points U and P. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.92", "dataset": "MATH"}
{"messages": [{"content": "QE = 5. Let K be the midpoint of segment EQ. Point J is obtained by rotating point Q by angle 2pi/3 about point E. Point M is obtained by rotating point E by angle 2pi/3 about point J. Let R be the rotation of point K by angle pi/2 around point M. Let Y be the midpoint of segment KR. Point V is the reflection of point Q across point M. Line T is the angle bisector of angle VQE. Line S is the reflection of line T across point M. Point N is the reflection of point Y across point R. Point P is the reflection of point J across line S. Find the distance between points P and N. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.49", "dataset": "MATH"}
{"messages": [{"content": "ES = 7. Point A is obtained by rotating point S by angle 5pi/12 about point E. Let X be the line through points S and A. Point Y is the reflection of point A across segment SE. Point I is the midpoint of segment SE. Line W passes through point A perpendicular to line X. Point N is the reflection of point I across line W. Let D be the line through points Y and N. Point L is the reflection of point Y across line X. Point C is the reflection of point L across line D. Point P is the intersection of segments SE and CL. What is the distance between points N and P? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.32", "dataset": "MATH"}
{"messages": [{"content": "Let HV = 8. Let T be the midpoint of segment VH. Point E is obtained by rotating point T by angle pi/6 about point V. Let M be the rotation of point T by angle pi/2 around point H. Let X be the reflection of point H across point M. Point J is the midpoint of segment EX. Point I is the reflection of point J across point X. Point Q is the midpoint of segment ME. Find the distance between points Q and I. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.83", "dataset": "MATH"}
{"messages": [{"content": "RZ = 11. Point Q is the midpoint of segment RZ. Let F be the rotation of point Q by angle 7pi/12 around point R. Point A is the reflection of point R across point Z. Let L be the reflection of point A across point Q. Let W be the reflection of point F across point R. Let U be the rotation of point Q by angle 5pi/12 around point Z. Point G is the reflection of point F across segment LQ. Point J is the midpoint of segment UG. Point N is the midpoint of segment WJ. Point Y is the midpoint of segment GN. Find the distance between points N and Y. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.09", "dataset": "MATH"}
{"messages": [{"content": "YW = 10. Point E is obtained by rotating point Y by angle 11pi/12 about point W. Let P be the midpoint of segment YE. Let K be the angle bisector of angle EPW. Point T is the reflection of point E across line K. Let Q be the line through point T perpendicular to line K. Let C be the angle bisector of angle PET. Line H passes through points E and W. Let U be the reflection of line H across line C. Line S is the reflection of line Q across line U. Let M be the reflection of line K through point E. Line L is the reflection of line M across line S. Point X is the reflection of point P across line L. What is the length of segment PX? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33.17", "dataset": "MATH"}
{"messages": [{"content": "OD = 7. Point H is obtained by rotating point D by angle pi/4 about point O. Point X is the reflection of point H across point D. Line M passes through points X and H. Point G is the reflection of point O across line M. Point C is the reflection of point G across point O. Find the distance between points C and H. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.59", "dataset": "MATH"}
{"messages": [{"content": "WP = 6. Point M is the midpoint of segment WP. Point I is obtained by rotating point P by angle pi/12 about point M. Point B is the midpoint of segment IM. Let U be the reflection of point B across point M. Let X be the angle bisector of angle UMB. Point S is the midpoint of segment PU. Point R is the reflection of point S across line X. Point A is the midpoint of segment RM. Point K is the midpoint of segment UA. Point O is the reflection of point W across line X. Find the length of segment KO. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.92", "dataset": "MATH"}
{"messages": [{"content": "PU = 3. Let Z be the rotation of point U by angle pi/6 around point P. Let O be the rotation of point P by angle pi/2 around point U. Let T be the reflection of point Z across point O. Point Y is the midpoint of segment OU. Point A is the reflection of point Z across point U. Let C be the midpoint of segment TO. Let M be the line through points A and O. Point K is the reflection of point T across line M. Let J be the line through points Y and T. Let R be the line through point K parallel to line M. Lines J and R intersect at point S. Point I is the reflection of point C across line R. Let F be the midpoint of segment IC. Let W be the midpoint of segment SF. Find the distance between points W and F. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.49", "dataset": "MATH"}
{"messages": [{"content": "Let LB = 12. Point O is the midpoint of segment LB. Point A is the reflection of point O across point L. Let T be the perpendicular bisector of segment AL. Let G be the line through point O parallel to line T. Let H be the rotation of point L by angle 2pi/3 around point O. Let V be the reflection of line T across line G. Let P be the line through points O and H. Point D is the midpoint of segment LH. Line K is the reflection of line P across point L. Point X is the reflection of point L across line P. Point R is the reflection of point D across line P. Let Q be the reflection of line V through point L. Point U is the reflection of point X across line K. Point E is the reflection of point D across line V. Let J be the midpoint of segment XR. Point Y is the intersection of segment JU and line Q. Find the distance between points E and Y. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40.99", "dataset": "MATH"}
{"messages": [{"content": "Let VS = 10. Point C is the reflection of point S across point V. Let B be the midpoint of segment SV. Let G be the rotation of point S by angle pi/12 around point B. Point L is the reflection of point G across segment BS. Point H is the midpoint of segment CG. Line M is the perpendicular bisector of segment CV. Point Z is the reflection of point L across line M. Find the distance between points Z and H. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.84", "dataset": "MATH"}
{"messages": [{"content": "Let OW = 11. Line Y is the perpendicular bisector of segment OW. Line P passes through point W parallel to line Y. Point T is the reflection of point O across line P. Point V is the reflection of point W across point T. Line A passes through points W and T. Let U be the rotation of point V by angle 5pi/6 around point W. Let S be the rotation of point O by angle pi/6 around point U. Let C be the midpoint of segment UO. Let R be the rotation of point V by angle 5pi/12 around point C. Let F be the reflection of point C across point W. Line G passes through point R perpendicular to line A. Point L is the reflection of point F across line A. Point I is the reflection of point L across line G. Find the distance between points I and S. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.71", "dataset": "MATH"}
{"messages": [{"content": "SZ = 6. Let A be the perpendicular bisector of segment SZ. Line K passes through point S parallel to line A. Point U lies on line K. Let W be the midpoint of segment SU. Let G be the reflection of point W across point Z. Point X is the reflection of point G across line K. What is the distance between points G and X? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.0", "dataset": "MATH"}
{"messages": [{"content": "Let NF = 1. Let H be the rotation of point F by angle 11pi/12 around point N. Let I be the midpoint of segment HN. Let D be the rotation of point I by angle 5pi/6 around point H. Let S be the midpoint of segment HD. Point G is the midpoint of segment SN. Point T is the midpoint of segment DG. Let M be the midpoint of segment GT. What is the length of segment MN? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.82", "dataset": "MATH"}
{"messages": [{"content": "Let IX = 2. Point D is the midpoint of segment IX. Let C be the rotation of point I by angle 2pi/3 around point D. Point U is obtained by rotating point X by angle 11pi/12 about point D. Let M be the midpoint of segment XC. Point S is the midpoint of segment DI. Point N is the reflection of point X across segment SM. Let L be the midpoint of segment MN. Point H is the reflection of point U across segment IX. Find the length of segment HL. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
{"messages": [{"content": "LX = 5. Let S be the midpoint of segment XL. Let T be the rotation of point L by angle 5pi/6 around point X. Line F passes through point T perpendicular to segment LX. Let P be the line through point T perpendicular to line F. Let O be the reflection of point S across point X. Point N is the reflection of point L across line P. Let M be the perpendicular bisector of segment LO. Let Y be the reflection of line M through point T. Point B is the reflection of point N across line Y. Find the distance between points S and B. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.77", "dataset": "MATH"}
{"messages": [{"content": "Let CS = 5. Let B be the perpendicular bisector of segment CS. Line N passes through point C parallel to line B. Let G be the rotation of point S by angle 11pi/12 around point C. Let K be the rotation of point G by angle pi around point S. Point M is the reflection of point C across point K. Point Z is the reflection of point K across segment MG. Line N and segment MG intersect at point P. Find the length of segment PZ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.97", "dataset": "MATH"}
{"messages": [{"content": "Let XT = 4. Line I is the perpendicular bisector of segment XT. Let F be the rotation of point T by angle pi/6 around point X. Line K passes through point F perpendicular to line I. Point B is the reflection of point T across point X. Let P be the reflection of point F across point B. Let H be the midpoint of segment BX. Let A be the midpoint of segment HP. Point R is the reflection of point T across line K. Point G is the reflection of point R across point A. Point Y is the reflection of point F across segment HP. What is the length of segment GY? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.21", "dataset": "MATH"}
{"messages": [{"content": "GV = 1. Point H is obtained by rotating point G by angle pi/2 about point V. Let W be the midpoint of segment GV. Line X is the angle bisector of angle HWV. Point D is obtained by rotating point W by angle 5pi/12 about point G. Line O passes through point H parallel to line X. Point F is the midpoint of segment DV. Let Z be the midpoint of segment WF. Let L be the reflection of line O across line X. Point Q is the reflection of point F across line L. Let N be the reflection of point Z across point G. Let J be the midpoint of segment DN. Find the length of segment JQ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.31", "dataset": "MATH"}
{"messages": [{"content": "JB = 12. Let F be the reflection of point B across point J. Let G be the perpendicular bisector of segment BJ. JI = 11. Line H passes through point J perpendicular to segment BJ. Point U is the reflection of point I across line H. Let O be the reflection of point U across point B. Point P is the reflection of point O across line G. Let R be the midpoint of segment FP. Find the length of segment FR. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.5", "dataset": "MATH"}
{"messages": [{"content": "QU = 6. Let R be the rotation of point Q by angle 5pi/6 around point U. Let B be the midpoint of segment UR. Line F is the perpendicular bisector of segment QU. Point A is the reflection of point B across line F. Let C be the midpoint of segment BU. Point J is the reflection of point R across segment BA. Find the distance between points C and J. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.97", "dataset": "MATH"}
{"messages": [{"content": "Let AC = 3. Point F is the reflection of point C across point A. Let K be the midpoint of segment AC. Point N is obtained by rotating point F by angle 5pi/12 about point K. Let Z be the rotation of point F by angle pi/12 around point C. Line D passes through points Z and N. Let W be the reflection of point A across point Z. Point T is the reflection of point C across segment ZW. Let B be the midpoint of segment TZ. Point Q is the reflection of point T across line D. Let Y be the midpoint of segment TB. Let P be the reflection of point A across point Q. What is the distance between points P and Y? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.46", "dataset": "MATH"}
{"messages": [{"content": "ZI = 6. ZD = 12. Let L be the midpoint of segment DZ. Let O be the vector from point L to point D. Point H is obtained by rotating point D by angle pi/6 about point L. Point B is the translation of point I by vector O. Let W be the line through points Z and B. Line A passes through point H parallel to line W. Let J be the line through point D perpendicular to line A. Point U is the reflection of point H across line J. Point M is the reflection of point D across line W. Point F is the reflection of point D across segment MU. Find the distance between points U and F. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.11", "dataset": "MATH"}
{"messages": [{"content": "Let FJ = 10. Let O be the rotation of point F by angle 5pi/12 around point J. Let Z be the midpoint of segment JO. Let R be the midpoint of segment JZ. Let Y be the midpoint of segment RF. What is the distance between points Y and Z? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.42", "dataset": "MATH"}
{"messages": [{"content": "Let YR = 2. Let W be the midpoint of segment YR. Point L is obtained by rotating point W by angle pi/12 about point R. Line X is the perpendicular bisector of segment WL. Line K is the reflection of line X across point Y. Let H be the rotation of point W by angle 5pi/6 around point Y. Let F be the line through point Y perpendicular to line K. Point N is the midpoint of segment RW. Point P is the reflection of point N across point W. Point D is obtained by rotating point H by angle 11pi/12 about point P. Point B is the reflection of point P across line F. Point V is the reflection of point B across segment RW. Line S is the angle bisector of angle PDV. Let E be the reflection of line S through point N. Point J is the midpoint of segment DH. Point C is the reflection of point J across line E. What is the distance between points W and C? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.24", "dataset": "MATH"}
{"messages": [{"content": "IQ = 12. Let F be the rotation of point Q by angle 5pi/12 around point I. Point R is the midpoint of segment IQ. Point L is obtained by rotating point Q by angle 2pi/3 about point R. Line T is the angle bisector of angle QRL. Let J be the reflection of point Q across point I. Point O is the reflection of point F across line T. Let C be the vector from point J to point I. Let W be point F translated by vector C. Let B be the line through point O perpendicular to line T. Let V be the perpendicular bisector of segment QI. Point X is the reflection of point F across line V. Line U passes through point W parallel to line B. Point E is the reflection of point X across line U. Point M is the midpoint of segment EX. Find the distance between points M and X. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.11", "dataset": "MATH"}
{"messages": [{"content": "Let ZP = 3. Point H is the reflection of point Z across point P. Line N is the perpendicular bisector of segment ZH. Point T lies on line N at distance 9 from point H. Let G be the reflection of point T across point P. Let E be the reflection of point G across point T. Let B be the midpoint of segment EZ. What is the length of segment GB? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.55", "dataset": "MATH"}
{"messages": [{"content": "BU = 12. Line D is the perpendicular bisector of segment UB. Let G be the midpoint of segment UB. Let I be the midpoint of segment GB. Line T is the perpendicular bisector of segment GB. Point M is the midpoint of segment UI. Let V be the line through point B parallel to line T. Let Q be the rotation of point G by angle 11pi/12 around point M. Point E is the reflection of point Q across point M. Point C is the reflection of point Q across line V. Line J is the reflection of line D across point E. Let S be the angle bisector of angle CEM. Point O is the reflection of point C across line S. Let X be the angle bisector of angle GOM. Line W is the reflection of line X across point G. Point L is the intersection of lines J and W. Point R is the reflection of point L across line X. What is the length of segment QR? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.81", "dataset": "MATH"}
{"messages": [{"content": "UK = 5. Point E is on segment UK. Point C is the midpoint of segment EK. T is constructed so that KT = 3. Let V be the midpoint of segment CK. Let Q be the reflection of point T across point V. Point Z is the reflection of point C across segment TQ. Find the length of segment QZ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "RD = 9. Let K be the reflection of point D across point R. Point W is obtained by rotating point D by angle 3pi/4 about point K. Line P passes through points W and D. Line H is the perpendicular bisector of segment KW. Point M is the reflection of point K across point D. Let A be the line through point R parallel to line H. Point E is the reflection of point M across point W. Point L is the intersection of lines A and P. Find the distance between points L and E. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76.57", "dataset": "MATH"}
{"messages": [{"content": "Let IF = 9. Point H is obtained by rotating point F by angle 5pi/6 about point I. Let R be the rotation of point F by angle pi around point I. Let G be the midpoint of segment IH. Let B be the reflection of point G across point R. Point Q is obtained by rotating point H by angle pi/4 about point R. Let D be the rotation of point Q by angle pi/6 around point B. Let P be the reflection of point R across point Q. Line Z passes through points P and I. Point W is the reflection of point R across line Z. Line U is the perpendicular bisector of segment DW. Point L is the midpoint of segment IB. Point A is the reflection of point F across line U. Point J is the reflection of point L across line U. Find the length of segment JA. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.09", "dataset": "MATH"}
{"messages": [{"content": "NV = 8. Let D be the perpendicular bisector of segment VN. Let U be the vector from point V to point N. Let X be the rotation of point V by angle 5pi/12 around point N. Line B passes through points N and X. Point J is the translation of point N by vector U. Point Y is the reflection of point J across line D. Line S is the reflection of line D across line B. Point I is the reflection of point Y across line B. Lines S and B intersect at point O. Point G is the reflection of point Y across point O. What is the distance between points G and I? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.63", "dataset": "MATH"}
{"messages": [{"content": "RB = 1. Let T be the rotation of point R by angle 7pi/12 around point B. Line A is the angle bisector of angle RBT. Point G is obtained by rotating point R by angle 11pi/12 about point T. Point L is the reflection of point R across point G. Point K is the reflection of point G across line A. Let Y be the line through points T and K. Point S is the reflection of point L across point K. Let M be the reflection of line Y through point R. Point F is the reflection of point S across line M. What is the distance between points L and F? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.32", "dataset": "MATH"}
{"messages": [{"content": "Let CP = 12. Point E is obtained by rotating point C by angle pi/4 about point P. Let N be the rotation of point E by angle 11pi/12 around point P. Line G is the angle bisector of angle NEC. Point X is the reflection of point P across line G. Let M be the reflection of point X across point E. Point Y is the midpoint of segment PC. Let W be the midpoint of segment MY. Find the distance between points W and M. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.04", "dataset": "MATH"}
{"messages": [{"content": "KL = 3. Line Q passes through points L and K. Let J be the rotation of point L by angle 11pi/12 around point K. Point D is the reflection of point J across point L. Line W is the angle bisector of angle KDJ. Line P is the reflection of line Q across line W. Point V is obtained by rotating point J by angle pi/3 about point K. Point X is obtained by rotating point L by angle pi/3 about point K. Line M is the perpendicular bisector of segment VX. Point O is the reflection of point L across line P. Let U be the reflection of point D across point J. Point E is the midpoint of segment UX. Point C is the reflection of point J across line M. Let H be the angle bisector of angle KLE. Point F is the reflection of point C across line H. Find the distance between points F and O. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.97", "dataset": "MATH"}
{"messages": [{"content": "TX = 7. Let U be the vector from point T to point X. Let O be point X translated by vector U. Let V be the reflection of point O across point T. Point Y is obtained by rotating point O by angle pi/4 about point X. Let C be point O translated by vector U. Point M is the reflection of point V across point Y. Let P be the midpoint of segment CY. Segments MT and CY intersect at point G. Find the distance between points G and P. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.58", "dataset": "MATH"}
{"messages": [{"content": "Let MV = 1. Let Y be the reflection of point M across point V. Point L is the reflection of point V across point Y. Point X is the reflection of point V across point M. Line F is the perpendicular bisector of segment VL. Let W be the midpoint of segment YX. Point I is on line F with |IM| = 5. Point E is the reflection of point W across line F. Line Q passes through point I parallel to segment YX. Line T passes through point E perpendicular to segment YX. Point C is the reflection of point V across line T. Point P is the reflection of point C across line Q. Point H is the midpoint of segment EM. Point J is the reflection of point H across segment CI. Point S is the reflection of point P across segment EI. What is the length of segment SJ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.38", "dataset": "MATH"}
{"messages": [{"content": "PR = 12. Let F be the vector from point R to point P. Let O be the reflection of point P across point R. Point B is obtained by rotating point P by angle pi/12 about point O. Point X is the translation of point P by vector F. Let Z be the rotation of point B by angle 7pi/12 around point P. Point E is the midpoint of segment ZO. Point I is the reflection of point P across segment ZO. Point H is the reflection of point Z across segment RP. Point Q is the midpoint of segment HR. Let N be the reflection of point Q across point R. Let L be the reflection of point N across point I. Let W be the line through point E parallel to segment RP. Point D is the reflection of point X across line W. Find the distance between points L and D. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.95", "dataset": "MATH"}
{"messages": [{"content": "Let WJ = 12. Let D be the rotation of point W by angle pi around point J. Line S is the angle bisector of angle DWJ. Line U passes through point J perpendicular to line S. Point M is on line U with |MJ| = 11. Let C be the perpendicular bisector of segment MD. Line I is the reflection of line C across point D. Point R is the midpoint of segment JD. Line P is the reflection of line C across line S. Let X be the reflection of line I across line P. Point L is the intersection of lines X and I. What is the distance between points R and L? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.46", "dataset": "MATH"}
{"messages": [{"content": "QA = 6. Let N be the reflection of point A across point Q. Let C be the angle bisector of angle NQA. Let O be the line through point A parallel to line C. Line H is the reflection of line O across line C. Point U is the reflection of point A across line H. Point V is the reflection of point U across point Q. Let E be the perpendicular bisector of segment UN. Let Z be the rotation of point U by angle pi/12 around point Q. Let Y be the midpoint of segment VZ. Let T be the midpoint of segment QA. Point G is the reflection of point T across line E. Point X is the midpoint of segment TG. What is the distance between points Y and X? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.53", "dataset": "MATH"}
{"messages": [{"content": "Let SE = 8. Point V is the midpoint of segment ES. Let D be the reflection of point V across point S. Point U is the midpoint of segment SV. Let Q be the perpendicular bisector of segment US. Point J is obtained by rotating point U by angle 11pi/12 about point V. Point C is the reflection of point D across line Q. Let P be the reflection of point C across point J. Point N is the midpoint of segment UP. Point H is the reflection of point C across segment UP. Let T be the midpoint of segment HN. What is the distance between points T and P? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "CD = 10. Let L be the rotation of point C by angle pi/4 around point D. Let W be the midpoint of segment DC. Let V be the reflection of point D across point L. Point I is the midpoint of segment LD. Let K be the reflection of point V across point I. Point T is the reflection of point W across point K. Point Z is the midpoint of segment LW. Point A is the midpoint of segment TD. Point Q is the reflection of point A across segment LW. Find the length of segment QZ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.87", "dataset": "MATH"}
{"messages": [{"content": "Let XO = 6. Point S is obtained by rotating point O by angle 7pi/12 about point X. Line Y is the perpendicular bisector of segment XS. Let V be the perpendicular bisector of segment SO. Let F be the rotation of point O by angle 3pi/4 around point S. Let A be the reflection of line V through point S. Point C is the reflection of point O across line Y. Let W be the midpoint of segment OF. Line U passes through points F and S. Line M is the reflection of line A across point C. Point Q is the reflection of point W across line U. Point D is the reflection of point Q across point F. Point P is the reflection of point D across line M. Point H is the reflection of point P across line Y. Point Z is the reflection of point P across line V. What is the distance between points H and Z? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33.62", "dataset": "MATH"}
{"messages": [{"content": "PA = 7. Point I is the midpoint of segment AP. Point B is the reflection of point A across point P. Point N is the midpoint of segment IA. Let T be the midpoint of segment IB. Line D is the perpendicular bisector of segment NB. Point G is on line D with |GI| = 9. Let U be the angle bisector of angle GTI. Point Y is the reflection of point N across line U. Point C is the reflection of point T across segment BG. Find the distance between points Y and C. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.13", "dataset": "MATH"}
{"messages": [{"content": "Let QX = 11. Point B is the midpoint of segment QX. Let F be the reflection of point B across point Q. Point Y is obtained by rotating point X by angle pi/12 about point B. Point G is the midpoint of segment YB. Let C be the rotation of point Y by angle 11pi/12 around point F. Point A is obtained by rotating point X by angle 5pi/12 about point C. Point N is the reflection of point F across segment YG. Point K is obtained by rotating point N by angle pi/6 about point Y. Let R be the reflection of point G across point X. Point T is the reflection of point A across point R. Point M is the midpoint of segment KA. What is the length of segment TM? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62.61", "dataset": "MATH"}
{"messages": [{"content": "RT = 1. Let C be the rotation of point T by angle 11pi/12 around point R. Let L be the rotation of point C by angle 11pi/12 around point R. Point V is the reflection of point L across point C. Line O is the angle bisector of angle VTL. Let Y be the line through point L perpendicular to line O. Let N be the rotation of point R by angle 5pi/6 around point V. Point F is the reflection of point N across line Y. Let D be the midpoint of segment LN. Point H is the reflection of point F across segment CN. What is the length of segment DH? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.9", "dataset": "MATH"}
{"messages": [{"content": "Let ZQ = 8. B is placed 7 units away from Q. Let C be the vector from point Q to point Z. Let I be the rotation of point B by angle pi around point Q. Point S is the translation of point I by vector C. Let H be the rotation of point Z by angle pi/3 around point Q. Point G is the reflection of point I across point H. Let F be the rotation of point Z by angle 3pi/4 around point H. Let Y be the midpoint of segment GS. Point A is the reflection of point F across segment SB. Line U is the perpendicular bisector of segment SB. Point K is the reflection of point A across line U. What is the length of segment KY? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.42", "dataset": "MATH"}
{"messages": [{"content": "WA = 9. Line O is the perpendicular bisector of segment AW. Line D passes through point W parallel to line O. Point B is the reflection of point A across line D. Let X be the reflection of point B across point A. Let K be the reflection of point X across point B. Let U be the rotation of point A by angle 7pi/12 around point W. Point Z is obtained by rotating point A by angle 3pi/4 about point U. Point M is the reflection of point W across segment AZ. Let C be the midpoint of segment ZA. Let Q be the midpoint of segment CM. Let G be the reflection of point A across point Z. Let N be the midpoint of segment KG. Point V is the intersection of segments AZ and QN. What is the length of segment VX? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.19", "dataset": "MATH"}
{"messages": [{"content": "Let FW = 6. Line G is the perpendicular bisector of segment WF. Line D is the reflection of line G across point W. Point T is on line G. Let C be the reflection of point F across point T. Point K is on line D with |KT| = 2. Point Q is the reflection of point K across line G. Let M be the reflection of point T across point Q. Line H passes through point F perpendicular to segment FW. Point N is the reflection of point F across point M. Point A is the reflection of point N across line H. Find the length of segment CA. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.42", "dataset": "MATH"}
{"messages": [{"content": "NV = 8. W is placed 4 units away from V. Let NR = 8. Point A is the midpoint of segment RW. Point B is the midpoint of segment WN. Let G be the midpoint of segment AB. Let O be the midpoint of segment AG. What is the length of segment BO? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Let SA = 2. Let F be the rotation of point A by angle 11pi/12 around point S. Let O be the midpoint of segment FA. Point V is the reflection of point S across point A. Point X is the reflection of point O across segment AS. Point B is the midpoint of segment XO. Find the distance between points B and V. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.97", "dataset": "MATH"}
{"messages": [{"content": "SO = 3. Let J be the midpoint of segment OS. Point Q is the midpoint of segment JS. Point L is obtained by rotating point O by angle pi/12 about point Q. Point K is obtained by rotating point J by angle 5pi/12 about point Q. Point T is the midpoint of segment OK. Let M be the angle bisector of angle TLO. Line I passes through point T parallel to line M. Point E is the reflection of point K across line I. What is the length of segment TE? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.09", "dataset": "MATH"}
{"messages": [{"content": "AM = 10. Point P is the reflection of point A across point M. Point X is the midpoint of segment AM. Let H be the midpoint of segment PM. Let W be the rotation of point H by angle pi around point A. Let V be the rotation of point X by angle 3pi/4 around point H. Let T be the angle bisector of angle VWH. Line D is the perpendicular bisector of segment XA. Line L is the reflection of line D across line T. Point U is the reflection of point P across point W. Point Q is the reflection of point M across line L. Point O is obtained by rotating point U by angle 3pi/4 about point A. Point B is the reflection of point Q across segment WO. Point S is the reflection of point U across point A. Point K is the reflection of point B across line T. What is the distance between points K and S? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62.56", "dataset": "MATH"}
{"messages": [{"content": "Let TE = 3. Let H be the midpoint of segment TE. Let G be the vector from point T to point E. Point N is obtained by rotating point E by angle 2pi/3 about point H. Let L be the line through points E and H. Point A is the reflection of point E across point N. Point D is the midpoint of segment HT. Let M be the reflection of point N across point T. Point K is the translation of point M by vector G. Point Z is the reflection of point K across line L. Line X is the angle bisector of angle AMD. Let O be the midpoint of segment EZ. Point V is the reflection of point O across segment EM. Point W is the reflection of point V across line X. Find the length of segment VW. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.92", "dataset": "MATH"}
{"messages": [{"content": "DA = 8. Let V be the reflection of point A across point D. Let Y be the reflection of point D across point V. Let O be the rotation of point D by angle pi/6 around point V. Let F be the perpendicular bisector of segment VO. Let E be the midpoint of segment OV. Point U is the reflection of point V across segment EA. Point L is the reflection of point Y across line F. Let N be the reflection of point Y across point U. What is the length of segment LN? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.65", "dataset": "MATH"}
{"messages": [{"content": "Let CX = 2. Point P is the midpoint of segment XC. Let M be the midpoint of segment PX. Let D be the angle bisector of angle CPM. Let J be the midpoint of segment CP. Line I is the reflection of line D across point C. Line H is the reflection of line I across point J. Point T is the reflection of point C across line H. Find the distance between points C and T. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Let LV = 7. Point H is the reflection of point V across point L. Let F be the midpoint of segment LV. Point T is the midpoint of segment LH. Point R is obtained by rotating point T by angle 5pi/12 about point L. Point C is the midpoint of segment LR. Let Z be the rotation of point L by angle 3pi/4 around point V. Point G is the reflection of point C across point F. Let Y be the line through points Z and T. Point S is the intersection of line Y and segment LC. What is the length of segment GS? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.2", "dataset": "MATH"}
{"messages": [{"content": "CF = 1. Let R be the rotation of point C by angle 2pi/3 around point F. Line Y is the angle bisector of angle CFR. Let I be the reflection of line Y through point C. Point N is the midpoint of segment FR. Let S be the midpoint of segment CN. Point H is the reflection of point N across line I. Find the length of segment SH. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.68", "dataset": "MATH"}
{"messages": [{"content": "Let OP = 2. Point M is the reflection of point P across point O. Let B be the reflection of point M across point P. Line S is the perpendicular bisector of segment PM. Line A passes through point M parallel to line S. Let Q be the reflection of point O across point P. Let C be the reflection of line A across line S. Line I passes through point B parallel to line A. Let V be the midpoint of segment QM. Point T is the midpoint of segment PV. Let L be the reflection of line C across line I. Point N is the midpoint of segment TO. Line F is the reflection of line L across point N. Point X is the reflection of point B across line F. What is the distance between points X and B? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29.0", "dataset": "MATH"}
{"messages": [{"content": "Let WJ = 11. Let N be the midpoint of segment WJ. Point S is obtained by rotating point J by angle pi/6 about point W. Point P is the midpoint of segment NW. Let L be the reflection of point S across point P. Let I be the reflection of point L across point W. Find the measure of angle ISJ, in radians. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.83", "dataset": "MATH"}
{"messages": [{"content": "OG = 2. Point E is the midpoint of segment GO. Point N is obtained by rotating point O by angle 7pi/12 about point E. Let A be the perpendicular bisector of segment EN. Let B be the line through point O parallel to line A. Line H passes through point E perpendicular to line B. Let V be the rotation of point O by angle 2pi/3 around point N. Point D is obtained by rotating point E by angle pi/4 about point N. Point X is the reflection of point D across line H. Let P be the midpoint of segment XD. Let T be the angle bisector of angle NVP. Point S is the reflection of point P across line T. Find the distance between points S and P. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
{"messages": [{"content": "Let XJ = 5. Point Z is obtained by rotating point J by angle pi/3 about point X. Let B be the rotation of point J by angle 3pi/4 around point X. Point A is the reflection of point Z across point B. Point D is the midpoint of segment JB. Let Y be the perpendicular bisector of segment XZ. Point H is the reflection of point D across line Y. Find the distance between points H and A. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.91", "dataset": "MATH"}
{"messages": [{"content": "TF = 11. Let X be the reflection of point F across point T. Point M is obtained by rotating point F by angle 5pi/6 about point T. Line W is the angle bisector of angle FMX. Point B is the reflection of point X across line W. Let S be the reflection of point T across point M. Let R be the reflection of point S across point B. Let N be the midpoint of segment RB. What is the distance between points N and R? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.28", "dataset": "MATH"}
{"messages": [{"content": "Let FS = 8. Let X be the rotation of point F by angle pi/12 around point S. Point A is the midpoint of segment SX. Let Y be the line through points F and S. Let FE = 2. Line G is the reflection of line Y across point E. Point K is the reflection of point X across line G. Line Q is the angle bisector of angle FEA. Point Z lies on line Q. Let T be the line through point K perpendicular to line G. Point H is the reflection of point F across line T. Point R is the reflection of point H across segment ZF. What is the length of segment RF? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.55", "dataset": "MATH"}
{"messages": [{"content": "Let KF = 2. Let N be the midpoint of segment KF. Z is placed 11 units away from N. Line I is the perpendicular bisector of segment ZN. Point E is on line I. Point X is the reflection of point E across segment FZ. Let U be the line through points X and K. Point A is the reflection of point N across line U. What is the length of segment AK? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "HZ = 9. Let Q be the line through points Z and H. Point P lies on line Q. Point Y is the reflection of point Z across point H. Line F passes through point Z perpendicular to line Q. Let X be the midpoint of segment ZP. Point G is the reflection of point Y across line F. Line B is the perpendicular bisector of segment GX. Point K is the reflection of point Z across line B. Find the distance between points X and K. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.0", "dataset": "MATH"}
{"messages": [{"content": "Let VF = 10. Let H be the perpendicular bisector of segment VF. Let B be the rotation of point F by angle pi/4 around point V. Line A passes through points B and F. Line I passes through point V parallel to line A. Line P is the reflection of line H across point B. Let Y be the reflection of line P across line I. Line X is the reflection of line H across line Y. Point T is the midpoint of segment VF. Point J is the intersection of lines Y and X. Find the distance between points T and J. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.93", "dataset": "MATH"}
{"messages": [{"content": "Let IT = 9. Point X is the midpoint of segment TI. Point H is obtained by rotating point I by angle pi/4 about point T. Let W be the reflection of point H across point X. Line S is the perpendicular bisector of segment TI. Point E is the reflection of point W across line S. Line D is the reflection of line S across point W. Point J is obtained by rotating point E by angle pi/12 about point I. Line N passes through points J and T. Let Y be the reflection of line S through point E. Point C is the reflection of point I across line N. Let L be the line through points C and I. Point M is the intersection of lines Y and L. Point U is the intersection of line D and segment TI. What is the length of segment MU? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.51", "dataset": "MATH"}
{"messages": [{"content": "Let WB = 5. Let G be the reflection of point W across point B. Line I is the perpendicular bisector of segment WG. Point V lies on line I at distance 9 from point W. Let H be the midpoint of segment VB. Point O is the midpoint of segment HB. Point T is the midpoint of segment HG. Point A is the reflection of point T across line I. What is the distance between points O and A? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Let IJ = 7. Point H is obtained by rotating point I by angle pi/6 about point J. Line L is the perpendicular bisector of segment JI. Line T is the angle bisector of angle HJI. Let V be the line through point H parallel to line T. Let B be the reflection of line V across line T. Line P is the reflection of line T across line L. Let W be the midpoint of segment HI. Let E be the midpoint of segment JW. Point U is the reflection of point H across line B. Line M is the reflection of line V across point I. Point F is the midpoint of segment UJ. Point S is the intersection of lines P and M. Point Z is the reflection of point E across point F. Find the distance between points Z and S. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.66", "dataset": "MATH"}
{"messages": [{"content": "Let OH = 10. Let I be the midpoint of segment HO. Let C be the rotation of point I by angle 2pi/3 around point H. Point K is the midpoint of segment IC. Let U be the line through points C and H. Let F be the line through point C perpendicular to line U. Point Y is the reflection of point H across line F. What is the length of segment KY? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.01", "dataset": "MATH"}
{"messages": [{"content": "Let GB = 11. Let C be the line through points B and G. Let F be the rotation of point B by angle pi/3 around point G. Point I lies on line C. V is placed 10 units away from I. Let U be the perpendicular bisector of segment GI. Let J be the midpoint of segment FB. Point Q is the midpoint of segment JF. Point T is the reflection of point V across line U. Point D is the midpoint of segment QT. Let A be the midpoint of segment TG. Find the distance between points A and D. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.96", "dataset": "MATH"}
{"messages": [{"content": "AL = 8. Let J be the midpoint of segment LA. Point P is the reflection of point J across point A. Point S is obtained by rotating point A by angle 3pi/4 about point P. Let W be the midpoint of segment LS. Line V is the perpendicular bisector of segment AP. Point N is the reflection of point L across point A. Point T is the reflection of point L across line V. Point C is the reflection of point N across point T. What is the distance between points W and C? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.65", "dataset": "MATH"}
{"messages": [{"content": "UH = 9. Let A be the perpendicular bisector of segment UH. Line T passes through point H parallel to line A. Point P lies on line T. Let M be the midpoint of segment HP. Point C is the midpoint of segment UP. What is the distance between points M and C? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.5", "dataset": "MATH"}
{"messages": [{"content": "Let GT = 8. Point U is obtained by rotating point T by angle 5pi/12 about point G. Point M is the midpoint of segment TG. Let W be the line through points U and G. Let J be the reflection of line W through point T. Point X is the reflection of point T across point U. Point Y is the reflection of point G across line J. Line C is the reflection of line W across point X. Line V passes through point M parallel to line C. Let L be the reflection of line C across line V. Line L and segment YM intersect at point O. What is the distance between points O and Y? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.73", "dataset": "MATH"}
{"messages": [{"content": "Let GW = 8. Point A is obtained by rotating point W by angle pi/6 about point G. Let S be the midpoint of segment AW. Point P is the midpoint of segment AS. Line V passes through point P perpendicular to segment WG. Point E is the reflection of point G across line V. Point O is the reflection of point E across point P. Find the length of segment SO. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.47", "dataset": "MATH"}
{"messages": [{"content": "Let YJ = 12. Point A is obtained by rotating point J by angle 5pi/12 about point Y. Point Q is obtained by rotating point Y by angle pi/3 about point J. Let C be the vector from point J to point Y. Let U be the rotation of point Q by angle 7pi/12 around point Y. Let M be the perpendicular bisector of segment YU. Let K be point U translated by vector C. Let Z be the line through point K perpendicular to line M. Point W is the midpoint of segment AK. Let X be the line through point W parallel to line Z. Line N is the reflection of line Z across point W. Point F is the reflection of point J across line Z. Line O passes through points F and A. Let R be the reflection of line X across line N. Point I is the reflection of point W across line R. Point E is the reflection of point I across line O. What is the distance between points E and W? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.64", "dataset": "MATH"}
{"messages": [{"content": "GW = 9. Let H be the rotation of point G by angle pi/4 around point W. Point L is the midpoint of segment WG. Point C is the midpoint of segment HL. Point J is the reflection of point C across segment GW. What is the distance between points L and J? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.32", "dataset": "MATH"}
{"messages": [{"content": "YM = 1. Let L be the reflection of point M across point Y. Line G is the perpendicular bisector of segment LM. Let W be the midpoint of segment YL. Line O is the reflection of line G across point W. Point Z is the reflection of point Y across line O. Find the distance between points Z and Y. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "SP = 7. Let M be the rotation of point P by angle pi/12 around point S. Point D is obtained by rotating point M by angle pi/6 about point P. Let J be the perpendicular bisector of segment PS. Point F is obtained by rotating point M by angle pi about point S. Let C be the line through points F and S. Line E is the reflection of line C across line J. Point R is the reflection of point D across line E. Point Y is the midpoint of segment FR. Point A is the reflection of point D across point M. What is the length of segment AY? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.04", "dataset": "MATH"}
{"messages": [{"content": "AN = 4. Let W be the vector from point A to point N. Let K be the midpoint of segment NA. Let H be point K translated by vector W. Point B is obtained by rotating point K by angle 5pi/12 about point N. Let I be the midpoint of segment NK. Let Z be the line through point A perpendicular to segment HN. Point F is the reflection of point A across point B. Let J be the rotation of point N by angle pi/2 around point B. Let P be the line through point I parallel to line Z. Point S is the midpoint of segment FI. Point C is the reflection of point S across line P. Point X is the reflection of point A across point H. Point O is the reflection of point X across point J. What is the length of segment OC? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.96", "dataset": "MATH"}
{"messages": [{"content": "Let EA = 11. Point O is obtained by rotating point A by angle 5pi/12 about point E. Point C is the reflection of point E across point O. Let H be the reflection of point O across point C. Let N be the perpendicular bisector of segment AE. Point U is the reflection of point E across point H. Line I passes through point C perpendicular to line N. Point X is the reflection of point C across point E. Point D is the reflection of point U across line I. What is the distance between points D and X? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.78", "dataset": "MATH"}
{"messages": [{"content": "Let YB = 11. Point D is obtained by rotating point B by angle 7pi/12 about point Y. Let N be the perpendicular bisector of segment YB. Let J be the reflection of line N through point D. Let H be the reflection of line J through point Y. Point R is the reflection of point D across line H. Point G is the reflection of point R across segment DB. Find the distance between points Y and G. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.08", "dataset": "MATH"}
{"messages": [{"content": "MZ = 6. Point Q is the midpoint of segment MZ. Let G be the vector from point Z to point Q. Let N be the perpendicular bisector of segment ZQ. Let L be the line through points Z and Q. Point C is obtained by rotating point Q by angle pi/4 about point M. Let A be the perpendicular bisector of segment CZ. Line H is the reflection of line A across line L. Let V be point C translated by vector G. Line J is the reflection of line A across point C. Line T is the reflection of line N across point V. Line D is the reflection of line L across line H. Point R is the intersection of lines T and D. Point S is the intersection of segment ZV and line J. Find the length of segment RS. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.14", "dataset": "MATH"}
{"messages": [{"content": "DR = 6. Let C be the reflection of point R across point D. Let I be the line through points C and R. Line B passes through point D perpendicular to line I. Let M be the rotation of point D by angle 2pi/3 around point C. Let W be the line through point C perpendicular to line I. Point O is the reflection of point R across line W. Point J is the reflection of point M across point R. Let F be the reflection of point D across point J. Point Y is the midpoint of segment RF. Point Z is obtained by rotating point D by angle 3pi/4 about point C. Point X is the reflection of point Z across line B. Let A be the reflection of point X across point C. Point N is the midpoint of segment OJ. Let K be the reflection of point A across point N. What is the length of segment KY? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.42", "dataset": "MATH"}
{"messages": [{"content": "PU = 6. Point A is obtained by rotating point P by angle pi/6 about point U. Point V is the reflection of point P across point U. Point Y is obtained by rotating point V by angle pi/12 about point P. Point Z is the reflection of point V across point P. Let M be the reflection of point V across point Z. Point G is the midpoint of segment VU. Let R be the line through point M perpendicular to segment VP. Let D be the reflection of point P across point Z. Point Q is the reflection of point G across segment AZ. Line B passes through point P parallel to line R. Point T is the reflection of point D across segment YP. Point W is the reflection of point M across line B. Point S is the midpoint of segment QT. What is the length of segment WS? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44.29", "dataset": "MATH"}
{"messages": [{"content": "DW = 2. Let E be the midpoint of segment WD. Point K is the midpoint of segment EW. Let M be the rotation of point W by angle 3pi/4 around point D. Point H is the reflection of point K across point E. Let V be the reflection of point M across point D. Point T is the midpoint of segment VK. What is the distance between points T and H? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "Let MO = 10. Line S is the perpendicular bisector of segment OM. Let N be the rotation of point O by angle 3pi/4 around point M. Let T be the midpoint of segment MN. Point U is obtained by rotating point N by angle 5pi/12 about point T. Let R be the midpoint of segment UM. Point P is the midpoint of segment UT. Point H is the midpoint of segment NP. Let F be the reflection of line S through point H. Let Z be the perpendicular bisector of segment UH. Point L is the reflection of point R across line F. Let C be the reflection of line Z through point N. Point I is the reflection of point L across line C. Let V be the midpoint of segment MI. What is the length of segment UV? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.06", "dataset": "MATH"}
{"messages": [{"content": "Let AG = 4. Point H is the midpoint of segment GA. Let R be the vector from point G to point A. Let F be point A translated by vector R. Point N is obtained by rotating point F by angle pi/4 about point H. Point Q is the translation of point F by vector R. Line O is the perpendicular bisector of segment NH. Point T is the reflection of point G across line O. Let K be the rotation of point A by angle pi around point T. Line L is the angle bisector of angle AFK. Let Y be the line through point K parallel to line L. Let S be the midpoint of segment KN. Point P is the reflection of point Q across line Y. Find the distance between points S and P. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.46", "dataset": "MATH"}
{"messages": [{"content": "QA = 5. Point M is the reflection of point Q across point A. Line B passes through point Q perpendicular to segment QA. Line D is the reflection of line B across point M. Line X is the reflection of line D across line B. Let V be the perpendicular bisector of segment QA. Point I lies on line V. Point T is the reflection of point I across line X. What is the distance between points T and I? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45.0", "dataset": "MATH"}
{"messages": [{"content": "Let CD = 5. Point W is the midpoint of segment DC. Point K is obtained by rotating point C by angle pi/4 about point D. Point X is obtained by rotating point D by angle pi/2 about point W. Let H be the midpoint of segment XC. Let M be the midpoint of segment KW. Point T is the midpoint of segment HX. Let B be the reflection of point H across point M. What is the length of segment TB? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.71", "dataset": "MATH"}
{"messages": [{"content": "MY = 10. Point G is obtained by rotating point Y by angle 11pi/12 about point M. Line T is the perpendicular bisector of segment MG. Let F be the line through point Y parallel to line T. Point Q is the reflection of point G across line F. Line D passes through point Q parallel to line F. Line J is the reflection of line F across line D. Point N is the midpoint of segment QY. Point R is the reflection of point N across line J. Point A is the reflection of point R across segment MY. What is the length of segment AM? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78.48", "dataset": "MATH"}
{"messages": [{"content": "VJ = 9. Point A is the midpoint of segment VJ. Let C be the reflection of point J across point V. Let R be the rotation of point C by angle pi/2 around point A. Line Y is the angle bisector of angle RCJ. Point D is the reflection of point C across point R. Line L is the perpendicular bisector of segment CD. Point Q is the midpoint of segment RV. Line T is the reflection of line Y across line L. Point P is obtained by rotating point A by angle pi/2 about point V. Point X is obtained by rotating point A by angle 5pi/12 about point J. Point M is the midpoint of segment DX. Point H is the reflection of point M across line T. Let G be the reflection of point J across point Q. Point I is the reflection of point H across segment PA. Let N be the reflection of point I across point V. Find the distance between points G and N. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.33", "dataset": "MATH"}
{"messages": [{"content": "RD = 5. Let U be the vector from point R to point D. Point Y is obtained by rotating point D by angle 7pi/12 about point R. Let O be the midpoint of segment RY. Let X be point O translated by vector U. Point A is the translation of point Y by vector U. Point J is the midpoint of segment DX. Let H be the reflection of point J across point A. Let G be point X translated by vector U. Let Z be the reflection of point Y across point X. Point I is the reflection of point R across point Z. Let W be the angle bisector of angle GIX. Point E is the reflection of point J across line W. Line N passes through points Y and Z. Line M is the reflection of line W across point H. Let S be the line through point O perpendicular to line N. Point V is the midpoint of segment EO. Let B be the reflection of line S through point V. Lines B and M intersect at point L. What is the distance between points L and H? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.21", "dataset": "MATH"}
{"messages": [{"content": "CP = 6. Point A is obtained by rotating point P by angle pi/2 about point C. Let D be the rotation of point A by angle pi/4 around point P. Let Z be the perpendicular bisector of segment CP. Let H be the reflection of point A across point D. Line W is the reflection of line Z across point P. Point B is the reflection of point H across line W. Point V is the reflection of point B across segment HC. What is the distance between points B and V? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43.03", "dataset": "MATH"}
{"messages": [{"content": "TB = 7. Line C passes through points B and T. Point R is the midpoint of segment TB. Let W be the line through point T perpendicular to line C. Point J is on line W with |JT| = 6. Point S is the reflection of point J across line C. Point X is obtained by rotating point R by angle pi/6 about point S. Point Q is the reflection of point T across segment RX. Point O is the reflection of point J across segment RX. Let E be the midpoint of segment SO. What is the distance between points E and Q? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.71", "dataset": "MATH"}
{"messages": [{"content": "Let RY = 8. Point A is obtained by rotating point R by angle pi/3 about point Y. Let D be the rotation of point A by angle 7pi/12 around point R. Point X is obtained by rotating point A by angle pi/6 about point R. Line Q passes through points Y and D. Point P is the reflection of point A across line Q. Let U be the line through point Y perpendicular to line Q. Point W is the reflection of point X across line U. Point F is the reflection of point W across line Q. Find the length of segment FP. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.01", "dataset": "MATH"}
{"messages": [{"content": "Let VZ = 10. Let T be the rotation of point V by angle pi/6 around point Z. Let E be the rotation of point T by angle 7pi/12 around point Z. Let Q be the angle bisector of angle ETZ. Point X is the midpoint of segment EZ. Let K be the midpoint of segment TE. Point O is the reflection of point X across line Q. What is the length of segment KO? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.88", "dataset": "MATH"}
{"messages": [{"content": "YJ = 2. Point U is the midpoint of segment JY. Point M is the reflection of point Y across point J. Point Q is obtained by rotating point M by angle pi/6 about point Y. Point W is obtained by rotating point Q by angle pi/3 about point M. Let C be the rotation of point J by angle pi/4 around point W. Point K is the midpoint of segment CU. Segments CU and JW intersect at point O. Point N is the midpoint of segment KJ. Find the length of segment NO. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
{"messages": [{"content": "Let RW = 12. Point K is obtained by rotating point R by angle pi/3 about point W. Let O be the reflection of point R across point W. Point V is the reflection of point O across point R. Let H be the midpoint of segment KW. Point L is the reflection of point H across point V. Find the distance between points L and H. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66.81", "dataset": "MATH"}
{"messages": [{"content": "Let AN = 1. Let P be the rotation of point A by angle pi/12 around point N. Let H be the reflection of point P across point N. Let Y be the midpoint of segment NH. Point D is obtained by rotating point N by angle pi/12 about point H. Let I be the midpoint of segment NY. Line Q is the perpendicular bisector of segment DP. Let V be the rotation of point D by angle pi/2 around point P. Let E be the midpoint of segment IV. Line K passes through point V perpendicular to line Q. Point U is the reflection of point D across segment NA. Line L is the perpendicular bisector of segment NA. Point Z is the reflection of point P across line K. Point T is the reflection of point H across line L. Let B be the angle bisector of angle UPZ. Point F is the reflection of point E across line B. What is the length of segment TF? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "XB = 1. Point Q is obtained by rotating point B by angle 3pi/4 about point X. Let K be the vector from point X to point B. Let W be point Q translated by vector K. Let R be the rotation of point X by angle pi around point B. Point J is the midpoint of segment XB. Point H is the reflection of point Q across segment XR. Point A is the reflection of point W across point H. What is the length of segment AJ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.06", "dataset": "MATH"}
{"messages": [{"content": "Let GK = 3. Point R is obtained by rotating point K by angle pi/4 about point G. Let P be the midpoint of segment GR. Let I be the reflection of point G across point R. Line W passes through points I and R. Point O is the reflection of point P across point G. Let T be the line through points K and P. Let V be the reflection of line T across line W. Line N passes through point O parallel to segment GK. Let Z be the line through point I parallel to line N. Lines Z and V intersect at point X. What is the distance between points X and P? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.63", "dataset": "MATH"}
{"messages": [{"content": "YP = 7. Point H is on segment YP. Let X be the perpendicular bisector of segment HY. Point Z is the reflection of point P across line X. Point T is the reflection of point Z across point H. Point U is the midpoint of segment ZH. Point K is the reflection of point U across point H. What is the distance between points T and K? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Let ZS = 12. Let P be the reflection of point Z across point S. Let G be the reflection of point P across point Z. Let T be the reflection of point G across point P. Let A be the midpoint of segment ZS. Let W be the reflection of point S across point T. Find the distance between points W and A. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126.0", "dataset": "MATH"}
{"messages": [{"content": "GC = 12. Let W be the rotation of point C by angle 5pi/6 around point G. Point Z is obtained by rotating point C by angle pi/2 about point W. Point H is obtained by rotating point C by angle 11pi/12 about point W. Point X is the reflection of point C across point H. Point F is the midpoint of segment XH. Let N be the line through point H parallel to segment ZG. Point S is the reflection of point F across line N. Point R is the reflection of point H across point S. What is the distance between points R and H? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45.97", "dataset": "MATH"}
{"messages": [{"content": "Let ND = 11. Let Q be the midpoint of segment ND. Point V is obtained by rotating point N by angle pi/12 about point Q. Let K be the midpoint of segment NQ. Let J be the rotation of point D by angle pi/6 around point V. Let O be the line through points J and Q. Let C be the line through point K parallel to segment NV. Lines O and C intersect at point I. Let G be the midpoint of segment NV. What is the length of segment GI? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.23", "dataset": "MATH"}
{"messages": [{"content": "XL = 8. Point Y is the midpoint of segment XL. Let J be the reflection of point Y across point X. Point B is the midpoint of segment XY. Point Q is the reflection of point B across point L. What is the distance between points Q and J? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.0", "dataset": "MATH"}
{"messages": [{"content": "Let MR = 1. Let J be the midpoint of segment RM. Let P be the perpendicular bisector of segment MJ. Line A is the perpendicular bisector of segment RJ. Let T be the reflection of line P across line A. Let Q be the midpoint of segment JR. Line F is the perpendicular bisector of segment MQ. Point H is on line F with |HQ| = 12. Line S is the perpendicular bisector of segment HJ. Line K is the reflection of line S across point M. Point C is the reflection of point M across line T. Point L is the reflection of point M across line K. Find the distance between points L and C. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.22", "dataset": "MATH"}
{"messages": [{"content": "WF = 8. Point P is the reflection of point W across point F. Let Y be the reflection of point W across point P. Let E be the reflection of point Y across point F. Point V is the midpoint of segment EF. Point J is the midpoint of segment YF. Let I be the reflection of point J across point V. Let K be the reflection of point I across point W. Find the distance between points K and J. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.0", "dataset": "MATH"}
{"messages": [{"content": "KF = 2. Let R be the midpoint of segment KF. Let C be the midpoint of segment RK. Point Z is the midpoint of segment RF. Let P be the rotation of point R by angle 11pi/12 around point C. Let E be the midpoint of segment PZ. Let X be the midpoint of segment ZR. Point M is the midpoint of segment XC. What is the length of segment EM? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
{"messages": [{"content": "AE = 8. Point Q is the midpoint of segment AE. Let F be the reflection of point Q across point A. Let X be the vector from point F to point A. Point B is obtained by rotating point E by angle 5pi/12 about point Q. Let N be the perpendicular bisector of segment BQ. Let C be the rotation of point F by angle pi/12 around point A. Let H be point B translated by vector X. Point R is obtained by rotating point C by angle 3pi/4 about point F. Let P be point E translated by vector X. Point Z is the reflection of point C across line N. Let O be the angle bisector of angle PBZ. Let S be the line through point R parallel to line O. Point U is the reflection of point F across line S. Point W is the midpoint of segment UH. What is the length of segment UW? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.75", "dataset": "MATH"}
{"messages": [{"content": "Let XE = 8. Let Y be the rotation of point E by angle pi/12 around point X. Line V is the angle bisector of angle YEX. Point S is the reflection of point Y across point E. Point G lies on line V at distance 11 from point E. Let K be the reflection of line V through point S. Let N be the reflection of line K across line V. Line R passes through point G perpendicular to line N. Point M is the reflection of point Y across line R. What is the length of segment MS? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.17", "dataset": "MATH"}
{"messages": [{"content": "Let GW = 3. Let O be the rotation of point W by angle pi/4 around point G. Let B be the midpoint of segment OG. Let D be the midpoint of segment WG. Line X is the angle bisector of angle OGB. Let A be the midpoint of segment OB. Point R is the reflection of point A across point W. Point V is the midpoint of segment WR. Line L is the angle bisector of angle AGV. Let Q be the reflection of line L across line X. Let U be the reflection of line L across line Q. Let S be the line through points R and W. Point M is the intersection of segments VB and AD. Point J is the intersection of lines S and U. Let P be the reflection of point J across point M. Find the distance between points J and P. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "303.91", "dataset": "MATH"}
{"messages": [{"content": "UZ = 4. Point K is the reflection of point Z across point U. F is placed 4 units away from Z. Line N is the perpendicular bisector of segment ZK. Let M be the line through point F perpendicular to line N. Let G be the line through point K perpendicular to line M. Point X is the reflection of point U across line G. Point D is the reflection of point X across line N. What is the distance between points D and X? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.0", "dataset": "MATH"}
{"messages": [{"content": "Let RF = 3. Line K passes through point F perpendicular to segment FR. Point Q is the midpoint of segment FR. Line O is the angle bisector of angle RQF. Let I be the reflection of line K across line O. Let S be the midpoint of segment QF. Point X is the reflection of point S across line I. Line T is the perpendicular bisector of segment RX. Line V is the reflection of line T across point Q. Point Z is the reflection of point X across line V. What is the distance between points R and Z? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.5", "dataset": "MATH"}
{"messages": [{"content": "Let MC = 9. Point E is the midpoint of segment MC. Let V be the angle bisector of angle CEM. Let U be the angle bisector of angle CME. Point W lies on line V at distance 11 from point C. Point D is obtained by rotating point C by angle 5pi/6 about point W. Line Q passes through points D and C. Point T is the midpoint of segment DW. Point A is obtained by rotating point E by angle pi/3 about point T. Point S lies on line V at distance 8 from point W. Let O be the line through point T parallel to line Q. Line F is the reflection of line U across line O. Let L be the line through point M perpendicular to line F. Point R lies on line L at distance 11 from point A. Point X is the reflection of point R across line O. Point I is the reflection of point W across segment SX. Point P is the reflection of point M across segment SX. What is the distance between points I and P? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.88", "dataset": "MATH"}
{"messages": [{"content": "Let BG = 12. Let A be the midpoint of segment BG. Let W be the rotation of point B by angle 11pi/12 around point A. Point P is the reflection of point W across point G. Let V be the reflection of point G across point P. Point L is the reflection of point V across segment AP. Let Z be the midpoint of segment AP. Point K is the midpoint of segment ZL. What is the length of segment KA? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.14", "dataset": "MATH"}
{"messages": [{"content": "Let BZ = 12. Let U be the rotation of point B by angle pi/2 around point Z. Point A is the midpoint of segment ZU. Let V be the rotation of point A by angle pi/2 around point Z. Line H passes through points Z and V. Point C is the reflection of point A across line H. Point R is the midpoint of segment VC. Line X passes through point Z perpendicular to line H. Point E is the reflection of point R across line X. Let M be the midpoint of segment VE. Find the length of segment BM. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.58", "dataset": "MATH"}
{"messages": [{"content": "SK = 3. Let J be the midpoint of segment SK. Let Z be the line through points S and J. Let W be the rotation of point J by angle 5pi/6 around point K. Point Q is the reflection of point K across segment WJ. Point X is the reflection of point Q across line Z. Point U is the midpoint of segment SQ. Find the length of segment UX. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Let ND = 2. Line F is the perpendicular bisector of segment ND. Let T be the line through point D parallel to line F. Point H is the midpoint of segment ND. Let X be the vector from point H to point N. Point S is the midpoint of segment DH. Line E passes through point N parallel to line T. Point O is the translation of point N by vector X. Point K lies on line E at distance 7 from point N. Point G is the reflection of point S across line F. Point U is the reflection of point K across point D. Let B be the reflection of point U across point G. Let A be the midpoint of segment UO. Find the distance between points B and A. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.42", "dataset": "MATH"}
{"messages": [{"content": "Let ON = 10. Let U be the midpoint of segment ON. Line W is the perpendicular bisector of segment UO. Let B be the rotation of point N by angle 5pi/6 around point U. Let L be the line through point B parallel to line W. Point G is the reflection of point B across segment ON. Let A be the perpendicular bisector of segment GU. Line V is the reflection of line A across point U. Lines V and L intersect at point E. Point K is the reflection of point N across line V. Let Y be the reflection of point E across point G. Point F is the reflection of point K across point B. Point C is the reflection of point B across point F. Find the distance between points C and Y. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31.2", "dataset": "MATH"}
{"messages": [{"content": "Let JY = 2. Let X be the reflection of point Y across point J. Point D is the midpoint of segment JX. Point N is the midpoint of segment YD. Point I is the midpoint of segment XN. Point P is obtained by rotating point J by angle pi about point I. Line Q is the angle bisector of angle XPD. Let O be the rotation of point P by angle 5pi/6 around point D. Point V is the midpoint of segment OI. Let F be the reflection of line Q through point V. Let U be the line through point O parallel to line F. Point A is the intersection of segment XN and line U. Let S be the reflection of point V across point A. What is the distance between points I and S? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Let SN = 2. Let E be the rotation of point S by angle 5pi/12 around point N. Let V be the rotation of point N by angle 2pi/3 around point E. Let D be the rotation of point S by angle pi/6 around point E. Let C be the reflection of point N across point V. Let R be the reflection of point E across point N. Point X is the midpoint of segment CR. Point B is the reflection of point D across segment EN. Line W passes through point B perpendicular to segment XR. Point K is the reflection of point V across line W. What is the distance between points K and S? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.7", "dataset": "MATH"}
{"messages": [{"content": "DG = 2. Let S be the midpoint of segment DG. Let W be the reflection of point S across point D. Let Y be the angle bisector of angle WDG. Let Z be the reflection of line Y through point S. Line U is the reflection of line Z across line Y. Let B be the perpendicular bisector of segment SD. Line F is the reflection of line B across line Y. Point L is the reflection of point G across line U. Point C is the reflection of point S across line F. Find the distance between points C and L. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "XB = 5. Let K be the perpendicular bisector of segment XB. Point Z lies on line K at distance 2 from point B. Point L is the reflection of point Z across segment BX. Let G be the midpoint of segment LB. Let Q be the midpoint of segment GZ. Let F be the vector from point X to point Z. Let T be point Z translated by vector F. Point O is the midpoint of segment QG. Let Y be the midpoint of segment GB. Point P is the midpoint of segment GO. Point S is the midpoint of segment PY. Point J is the reflection of point T across segment BX. Let W be the reflection of point S across point B. Let N be the midpoint of segment JY. Find the length of segment NW. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.11", "dataset": "MATH"}
{"messages": [{"content": "SE = 12. Point Y is obtained by rotating point E by angle 7pi/12 about point S. Line H passes through points S and E. Line G passes through point E perpendicular to segment YS. Let K be the midpoint of segment YS. Let X be the line through point K parallel to line H. Point Z is the reflection of point S across line G. Let W be the rotation of point Z by angle pi/6 around point Y. Line L passes through point W perpendicular to line X. Point J is the reflection of point S across point E. Point B is the reflection of point J across line L. Point F is the midpoint of segment KJ. Let I be the reflection of point S across point F. What is the length of segment IB? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.52", "dataset": "MATH"}
{"messages": [{"content": "JZ = 4. Let D be the rotation of point Z by angle pi/2 around point J. Point K is the reflection of point J across point D. Let S be the rotation of point K by angle 3pi/4 around point D. Let L be the rotation of point J by angle pi around point Z. Point E is the reflection of point L across segment SD. Let A be the perpendicular bisector of segment DE. Point B is the reflection of point S across line A. Point G is the midpoint of segment SD. Line C passes through point B perpendicular to segment SD. Point V is the reflection of point K across segment SD. Point X is the reflection of point S across line C. Let U be the angle bisector of angle GDK. Point F is the reflection of point X across line U. Point Q is the reflection of point F across point D. Find the distance between points Q and V. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.16", "dataset": "MATH"}
{"messages": [{"content": "Let YJ = 1. Line N is the perpendicular bisector of segment YJ. Point K is obtained by rotating point Y by angle pi/12 about point J. Let F be the reflection of point K across point J. Let G be the vector from point F to point Y. Point W is the reflection of point F across line N. Point A is the translation of point W by vector G. Point I is the reflection of point A across point F. Point V is the reflection of point I across line N. Let Q be the line through points F and A. Let P be the angle bisector of angle KVA. Point R is the reflection of point J across line P. Point X is the reflection of point R across line Q. Find the distance between points R and X. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
{"messages": [{"content": "HM = 5. Point U is obtained by rotating point H by angle pi/3 about point M. Point J is the reflection of point M across point H. Line Q passes through points J and U. Point L is on line Q. Let K be the midpoint of segment JL. What is the measure of angle KJM, in radians? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.52", "dataset": "MATH"}
{"messages": [{"content": "LU = 6. Let J be the midpoint of segment UL. Point Z is the reflection of point J across point L. Let M be the perpendicular bisector of segment UL. Line T is the perpendicular bisector of segment LJ. Point G is the reflection of point L across point Z. Line O passes through point G parallel to line M. Point N is obtained by rotating point Z by angle 5pi/6 about point U. Let S be the midpoint of segment GN. Point A is the reflection of point S across line T. Point W is the reflection of point A across line O. Let C be the reflection of point W across point Z. Find the length of segment GC. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.33", "dataset": "MATH"}
{"messages": [{"content": "Let HO = 8. Line T is the perpendicular bisector of segment HO. Point P is the midpoint of segment OH. Let R be the rotation of point P by angle pi/6 around point O. Line A is the perpendicular bisector of segment HR. Line L is the reflection of line T across line A. Point Q is the intersection of line L and segment HR. Point B is the reflection of point H across line L. Find the distance between points B and Q. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.59", "dataset": "MATH"}
{"messages": [{"content": "Let ZX = 5. Let K be the midpoint of segment XZ. Let L be the reflection of point K across point Z. Line D is the angle bisector of angle ZKX. Point M is on line D. Let C be the reflection of line D through point Z. Point J is the reflection of point X across line C. Let P be the line through points M and L. Point Q is on line P. Point U is the reflection of point Q across point X. Point H is the reflection of point X across segment JU. Point T is the reflection of point Z across segment JU. Find the length of segment TH. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.0", "dataset": "MATH"}
{"messages": [{"content": "WX = 10. Let S be the midpoint of segment XW. Point L is the midpoint of segment SW. Line C is the perpendicular bisector of segment WL. Let N be the rotation of point W by angle 5pi/6 around point S. Line J passes through point X parallel to line C. Point M is the reflection of point N across line J. Point Q is the reflection of point S across line C. Let I be the midpoint of segment MX. What is the distance between points Q and I? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.9", "dataset": "MATH"}
{"messages": [{"content": "WT = 2. Let E be the vector from point T to point W. Point D is obtained by rotating point W by angle 2pi/3 about point T. Point C is the translation of point W by vector E. Point B is obtained by rotating point C by angle 5pi/12 about point D. Point S is the reflection of point D across point B. Point I is the midpoint of segment WB. Point F is the reflection of point S across point I. Let R be the reflection of point F across point B. Point A is the reflection of point R across segment CW. Find the length of segment SA. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.1", "dataset": "MATH"}
{"messages": [{"content": "AB = 10. Let S be the rotation of point B by angle pi/3 around point A. Point H is the midpoint of segment AS. Let P be the midpoint of segment SH. Let D be the midpoint of segment BS. Let T be the line through point D parallel to segment BP. Point U is the reflection of point P across line T. Point K is the reflection of point U across segment BP. Find the distance between points D and K. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.5", "dataset": "MATH"}
{"messages": [{"content": "Let WA = 2. Point U is obtained by rotating point A by angle pi/4 about point W. Let P be the angle bisector of angle WAU. Point G is the reflection of point W across point U. Let N be the angle bisector of angle WGA. Point L is the reflection of point U across point G. Line E passes through point U perpendicular to line P. Line J is the reflection of line E across line N. Segment AG and line J intersect at point B. What is the distance between points B and L? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.88", "dataset": "MATH"}
{"messages": [{"content": "Let NP = 4. Point K is obtained by rotating point N by angle 11pi/12 about point P. Point Y is the reflection of point K across point N. Let M be the rotation of point Y by angle pi/4 around point K. Let B be the reflection of point P across point Y. Point S is the midpoint of segment YN. Point O is the reflection of point S across segment NM. Find the distance between points O and B. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.22", "dataset": "MATH"}
{"messages": [{"content": "Let SO = 12. Line W is the perpendicular bisector of segment OS. Point V lies on line W at distance 9 from point O. Line G passes through point S parallel to line W. Point I is the midpoint of segment SO. Point A is the reflection of point O across line G. Point F is the midpoint of segment SA. Point U is the reflection of point I across point V. Find the length of segment FU. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.63", "dataset": "MATH"}
{"messages": [{"content": "Let ZJ = 7. Let S be the perpendicular bisector of segment ZJ. Point G is obtained by rotating point Z by angle 3pi/4 about point J. Let N be the rotation of point G by angle 11pi/12 around point Z. Point V is on line S with |VJ| = 11. Point R is the midpoint of segment VZ. Point X is the midpoint of segment GN. Let W be the reflection of point Z across point X. Point T is the reflection of point R across point X. Find the length of segment TW. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.77", "dataset": "MATH"}
{"messages": [{"content": "XZ = 4. Let N be the rotation of point Z by angle pi/12 around point X. Let D be the rotation of point Z by angle 3pi/4 around point N. Point O is the midpoint of segment ZD. Point T is the reflection of point N across segment ZD. Let H be the midpoint of segment DT. Find the length of segment OH. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.52", "dataset": "MATH"}
{"messages": [{"content": "IN = 5. Let C be the reflection of point N across point I. Let F be the rotation of point N by angle 11pi/12 around point C. Line O passes through points F and C. Let A be the midpoint of segment FN. Let Z be the angle bisector of angle CAN. Let R be the reflection of point I across point A. Let Q be the reflection of line O across line Z. Point Y is the intersection of lines O and Q. Find the distance between points R and Y. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.81", "dataset": "MATH"}
{"messages": [{"content": "Let ES = 1. Line G is the perpendicular bisector of segment ES. Point Z is obtained by rotating point E by angle 2pi/3 about point S. Let D be the reflection of point Z across point E. Line O passes through point E parallel to line G. Point P is the reflection of point Z across line O. Point T is the reflection of point P across segment EZ. Find the measure of angle DPT, in radians. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.52", "dataset": "MATH"}
{"messages": [{"content": "Let KP = 5. Let B be the vector from point P to point K. Let U be the line through points K and P. Let R be the line through point K perpendicular to line U. Point X is obtained by rotating point P by angle 7pi/12 about point K. Line E is the reflection of line R across point P. Let J be the vector from point X to point K. Point Q is the reflection of point P across line E. Point W is the translation of point Q by vector J. Line H passes through points P and X. Point S is the reflection of point P across point K. Let Z be point S translated by vector B. Point A is the reflection of point W across line H. Point N is obtained by rotating point W by angle 5pi/6 about point K. Point F is the reflection of point N across point P. Line M passes through point P parallel to segment ZX. Line M and segment KF intersect at point C. Find the distance between points C and A. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.06", "dataset": "MATH"}
{"messages": [{"content": "IX = 7. Let Y be the midpoint of segment XI. Let A be the rotation of point X by angle pi/3 around point I. Point J is the reflection of point X across point A. Point W is the midpoint of segment XA. Point Q is the reflection of point Y across segment IW. What is the measure of angle JWQ, in radians? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.05", "dataset": "MATH"}
{"messages": [{"content": "LG = 4. Let O be the line through points L and G. Let T be the perpendicular bisector of segment GL. Point Z is the reflection of point L across point G. Let V be the reflection of line T through point G. Point E is the intersection of lines O and V. Find the distance between points Z and E. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Let KA = 7. Let C be the midpoint of segment AK. Point Q is the reflection of point C across point A. Let U be the rotation of point K by angle 11pi/12 around point Q. Line H is the angle bisector of angle CAU. Line N is the reflection of line H across point C. Line Z is the perpendicular bisector of segment UC. Let E be the line through point U parallel to line N. Line D is the reflection of line Z across line H. Line M is the reflection of line E across point K. Let B be the line through point Q parallel to line M. Point O is the reflection of point A across line B. Point T is the reflection of point K across point O. Let R be the line through point T parallel to segment AQ. Lines R and D intersect at point P. Find the distance between points O and P. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.23", "dataset": "MATH"}
{"messages": [{"content": "OD = 4. Point L is the reflection of point O across point D. Let E be the rotation of point D by angle pi/4 around point L. Point R is obtained by rotating point O by angle 5pi/6 about point D. Let Y be the rotation of point O by angle pi/2 around point D. Let J be the reflection of point O across point E. Line G is the angle bisector of angle RYL. Point X is obtained by rotating point E by angle pi/12 about point J. Line B is the reflection of line G across point R. Line S passes through points L and D. Lines B and S intersect at point Z. Point K is the reflection of point X across point Z. Find the distance between points R and K. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.61", "dataset": "MATH"}
{"messages": [{"content": "Let RJ = 11. Let X be the rotation of point J by angle 7pi/12 around point R. Let K be the line through points R and J. Point I is the reflection of point R across point J. Let M be the reflection of point R across point X. Line D passes through point R perpendicular to line K. Point E is the midpoint of segment RX. Point Z is the midpoint of segment EI. Point C is the reflection of point Z across line D. Find the length of segment CM. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.15", "dataset": "MATH"}
{"messages": [{"content": "Let HR = 11. Point M is obtained by rotating point H by angle pi/3 about point R. Point B is the reflection of point R across point M. Point Z is the midpoint of segment MB. Let P be the angle bisector of angle ZMR. Point C is obtained by rotating point Z by angle 7pi/12 about point R. Let D be the midpoint of segment RM. Point V is the reflection of point C across point B. Point U is obtained by rotating point D by angle 5pi/12 about point V. Let L be the reflection of line P through point U. Line X is the reflection of line P across line L. Line N is the reflection of line X across point H. Point S is the reflection of point C across line N. What is the length of segment SD? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89.11", "dataset": "MATH"}
{"messages": [{"content": "VB = 6. Let H be the midpoint of segment BV. Line L is the perpendicular bisector of segment BH. Point Z lies on line L at distance 5 from point V. Let F be the midpoint of segment HV. Point U is the midpoint of segment FZ. Point E is the reflection of point V across point Z. Point T is the reflection of point U across point E. Point M is the midpoint of segment FE. Find the distance between points T and M. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.85", "dataset": "MATH"}
{"messages": [{"content": "DG = 7. Point V is obtained by rotating point D by angle pi/6 about point G. Let Z be the reflection of point G across point V. Let S be the line through point Z perpendicular to segment VZ. Point J is the reflection of point D across segment VZ. Point T is the reflection of point D across line S. Point R is the midpoint of segment VJ. Point N is the midpoint of segment RZ. Find the length of segment NT. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.47", "dataset": "MATH"}
{"messages": [{"content": "IP = 4. Let T be the line through points P and I. Let L be the vector from point P to point I. Point V is the reflection of point I across point P. Line W is the perpendicular bisector of segment VP. Let J be point I translated by vector L. Line A is the reflection of line W across point J. Let U be the line through point J parallel to line W. Let M be the reflection of point V across point J. Point S is the intersection of lines T and A. Point K is on line U with |KM| = 1. Line F passes through point S perpendicular to segment IK. Point Q is the reflection of point V across line F. Point C is the reflection of point M across segment IK. What is the distance between points C and Q? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.5", "dataset": "MATH"}
{"messages": [{"content": "MN = 6. Let L be the midpoint of segment NM. Let X be the midpoint of segment LN. Let K be the reflection of point X across point L. Point W is the midpoint of segment NK. Find the distance between points W and K. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "OC = 1. Point P is the reflection of point C across point O. Point N is the midpoint of segment CO. Let K be the rotation of point P by angle 11pi/12 around point C. Let B be the angle bisector of angle NKC. Point L is the reflection of point P across line B. Let S be the reflection of point L across point K. Let E be the midpoint of segment CK. Point A is the reflection of point E across segment LN. What is the length of segment AS? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.32", "dataset": "MATH"}
{"messages": [{"content": "FX = 2. Let P be the rotation of point X by angle 7pi/12 around point F. Point V is the midpoint of segment FP. Let E be the rotation of point P by angle 7pi/12 around point V. Point N is the midpoint of segment FX. Let Y be the line through point E perpendicular to segment NE. Point H is the reflection of point P across line Y. Let L be the reflection of point V across point H. What is the length of segment LE? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.77", "dataset": "MATH"}
{"messages": [{"content": "WU = 11. Point M is the midpoint of segment WU. Let I be the perpendicular bisector of segment WM. Point P is the reflection of point M across point U. Point R is obtained by rotating point U by angle 2pi/3 about point W. Point K is the reflection of point P across line I. Let H be the reflection of line I through point U. Line J is the perpendicular bisector of segment KW. Line F is the reflection of line J across line H. Point Q is the reflection of point R across line F. Point B is the reflection of point K across point Q. Point E is the reflection of point B across point R. Find the length of segment EB. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "407.45", "dataset": "MATH"}
{"messages": [{"content": "Let CD = 1. Let R be the reflection of point C across point D. Let W be the perpendicular bisector of segment RD. Let K be the reflection of line W through point R. Let G be the midpoint of segment CD. Point N is the midpoint of segment RG. Let O be the reflection of line W across line K. Line F is the reflection of line K across line O. Point J lies on line O at distance 6 from point G. Let H be the line through point N parallel to line F. Let M be the reflection of line H across line O. Point T is the reflection of point J across point G. Point X is the reflection of point T across line M. Find the distance between points N and X. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.09", "dataset": "MATH"}
{"messages": [{"content": "ZJ = 11. Line T passes through point Z perpendicular to segment JZ. Point O is the midpoint of segment ZJ. Point A is the reflection of point O across line T. Let R be the midpoint of segment ZO. What is the distance between points R and A? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.25", "dataset": "MATH"}
{"messages": [{"content": "ZO = 7. Let N be the perpendicular bisector of segment OZ. Let M be the line through point O parallel to line N. Point X lies on line M at distance 8 from point Z. Point V is the midpoint of segment XO. Line Q is the reflection of line N across point X. Point W is the reflection of point V across line Q. Point L is the reflection of point V across point X. What is the distance between points L and W? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.63", "dataset": "MATH"}
{"messages": [{"content": "SZ = 10. Point U is the midpoint of segment SZ. Let G be the line through point U perpendicular to segment ZU. Point T is the midpoint of segment ZU. Point E is the reflection of point T across line G. Find the distance between points E and U. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Let AZ = 5. Point J is the midpoint of segment ZA. Let D be the reflection of point Z across point A. Let W be the midpoint of segment JD. Let S be the midpoint of segment ZJ. Find the distance between points S and W. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.0", "dataset": "MATH"}
{"messages": [{"content": "NC = 2. Point I is obtained by rotating point N by angle pi/6 about point C. Point E is the reflection of point C across point I. Let L be the perpendicular bisector of segment EI. Let Z be the midpoint of segment EI. Let B be the perpendicular bisector of segment NE. Let M be the line through point E perpendicular to line L. Let O be the reflection of line B across line M. Point F is obtained by rotating point E by angle pi/6 about point N. Let X be the reflection of point F across point I. Line O and segment FX intersect at point K. Let V be the reflection of point K across point I. What is the distance between points Z and V? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.2", "dataset": "MATH"}
{"messages": [{"content": "CW = 3. Let A be the rotation of point C by angle 5pi/12 around point W. Let R be the rotation of point A by angle pi around point C. Let D be the vector from point W to point R. Let F be the midpoint of segment WA. Let B be point C translated by vector D. Let K be the perpendicular bisector of segment WR. Point P is the reflection of point B across line K. Point T is the reflection of point B across point P. Point X is the reflection of point A across segment BF. Find the distance between points T and X. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.2", "dataset": "MATH"}
{"messages": [{"content": "PH = 5. Let O be the midpoint of segment PH. Point W is obtained by rotating point P by angle pi/3 about point H. Point K is the reflection of point W across point P. Point R is the reflection of point W across point O. Point Z is the reflection of point O across point H. Let L be the angle bisector of angle ROK. Let X be the reflection of line L through point P. Point Q is the reflection of point Z across line X. Find the length of segment QR. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.57", "dataset": "MATH"}
{"messages": [{"content": "Let VT = 5. Let E be the rotation of point V by angle pi around point T. Point I is the midpoint of segment TV. Let H be the line through point I perpendicular to segment EI. Point G is the reflection of point E across line H. Point Q is the midpoint of segment EI. Find the distance between points Q and G. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.25", "dataset": "MATH"}
{"messages": [{"content": "Let DP = 2. Point F is the reflection of point P across point D. Let X be the reflection of point D across point F. Let U be the midpoint of segment FX. Line J is the perpendicular bisector of segment PU. Point M is the reflection of point X across line J. What is the distance between points M and F? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.0", "dataset": "MATH"}
{"messages": [{"content": "NT = 4. Let J be the midpoint of segment NT. Let Z be the reflection of point J across point T. Let L be the perpendicular bisector of segment NT. Line U is the perpendicular bisector of segment ZT. Let F be the rotation of point N by angle 5pi/12 around point T. Let O be the rotation of point J by angle 5pi/12 around point F. Point M is the reflection of point O across segment NT. Point S is the reflection of point O across line U. Point Y is the midpoint of segment JT. Line G is the reflection of line U across line L. Let C be the line through points Y and S. Lines G and C intersect at point V. What is the length of segment MV? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Let BL = 2. Let X be the reflection of point B across point L. Let Y be the line through points L and X. Line K passes through point L perpendicular to line Y. Point V lies on line K at distance 5 from point L. Let M be the midpoint of segment BV. Point Q is the reflection of point B across point X. Let W be the midpoint of segment MV. Let H be the reflection of point V across point L. Point C is the reflection of point W across point H. Find the distance between points Q and C. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.81", "dataset": "MATH"}
{"messages": [{"content": "Let OF = 5. Let M be the rotation of point F by angle 2pi/3 around point O. Let R be the midpoint of segment OM. Point Y is the midpoint of segment RO. Point N is the midpoint of segment FR. Point X is the reflection of point Y across segment FR. Find the length of segment NX. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Let KV = 4. Let F be the vector from point K to point V. Point R is the translation of point V by vector F. Point M is obtained by rotating point K by angle pi/3 about point V. Line O passes through point M perpendicular to segment KV. Let Q be the reflection of point K across point R. Line P is the perpendicular bisector of segment VQ. Point N is the translation of point Q by vector F. Let E be the midpoint of segment MN. Point A is the midpoint of segment KV. Let T be the line through point K parallel to line P. Line J is the reflection of line O across point E. Point Z is the reflection of point M across line J. Point I is the midpoint of segment ZQ. Point X is the midpoint of segment ZK. Let U be the angle bisector of angle INZ. Point C is the reflection of point I across line U. Point Y is the reflection of point E across line T. Let L be the angle bisector of angle CAY. Point G is the reflection of point E across line L. Point B is the reflection of point G across point I. Find the length of segment BX. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41.84", "dataset": "MATH"}
{"messages": [{"content": "PG = 2. Let E be the vector from point G to point P. Point V is obtained by rotating point G by angle 7pi/12 about point P. Let F be the reflection of point G across point P. Point T is the reflection of point G across point V. Let N be the reflection of point V across point T. Point U is the translation of point T by vector E. Let I be the rotation of point F by angle pi around point U. Line B passes through point I perpendicular to segment UP. Let D be the line through point N parallel to line B. Let R be the line through point T parallel to line D. Point Y is the reflection of point P across line R. Let J be the reflection of point Y across point I. Find the distance between points J and N. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.91", "dataset": "MATH"}
{"messages": [{"content": "Let HI = 11. Line R passes through point I perpendicular to segment IH. Point N is the reflection of point H across line R. Point B is obtained by rotating point H by angle pi about point N. Let V be the rotation of point B by angle 2pi/3 around point I. Let J be the line through point N parallel to line R. Line T is the reflection of line J across point V. Point K is the reflection of point V across segment IH. Point O is the reflection of point K across line J. Let E be the reflection of point N across point O. Point C is the reflection of point E across line T. Let Z be the reflection of point O across point H. Find the length of segment ZC. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126.86", "dataset": "MATH"}
{"messages": [{"content": "RE = 9. Line X passes through points E and R. Let A be the rotation of point E by angle pi/4 around point R. Let Y be the rotation of point A by angle pi/6 around point R. Point L is the midpoint of segment YE. Point C is the reflection of point E across point R. Let P be the midpoint of segment LY. Line G passes through point L parallel to line X. Let I be the reflection of line X across line G. Line S passes through points C and P. Lines S and I intersect at point H. Point K is the reflection of point R across point H. Find the distance between points Y and K. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.76", "dataset": "MATH"}
{"messages": [{"content": "PV = 10. Let C be the line through points V and P. Let F be the line through point V perpendicular to line C. Let K be the reflection of point V across point P. Point R is the midpoint of segment VP. Point X is the reflection of point R across line F. What is the distance between points X and K? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25.0", "dataset": "MATH"}
{"messages": [{"content": "Let ZX = 5. Let J be the perpendicular bisector of segment XZ. Line S is the reflection of line J across point Z. Point I is the reflection of point X across line S. Line T is the reflection of line S across line J. Let O be the midpoint of segment ZI. Point Y lies on line S at distance 1 from point O. Point A is the reflection of point O across line T. Let U be the line through point A perpendicular to segment XY. Let R be the reflection of line U through point O. Point D is the reflection of point A across line R. Point L is the reflection of point D across segment XY. Let W be the midpoint of segment XD. Point E is the reflection of point L across line J. What is the distance between points E and W? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120.43", "dataset": "MATH"}
{"messages": [{"content": "VH = 9. Point Q is the reflection of point H across point V. Let B be the rotation of point Q by angle pi/4 around point H. Let S be the rotation of point B by angle 2pi/3 around point V. Let Y be the rotation of point H by angle pi/2 around point S. Point K is obtained by rotating point V by angle 5pi/12 about point H. Point M is the midpoint of segment KY. Point X is the reflection of point M across segment BK. Let E be the midpoint of segment SH. What is the distance between points E and X? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.21", "dataset": "MATH"}
{"messages": [{"content": "MV = 3. Let I be the rotation of point M by angle 3pi/4 around point V. Let K be the reflection of point I across point M. Point N is the midpoint of segment KM. Point Y is the reflection of point N across point K. Let X be the perpendicular bisector of segment NM. Line R is the reflection of line X across point Y. Point W is the reflection of point Y across line R. Find the distance between points M and W. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.17", "dataset": "MATH"}
{"messages": [{"content": "AF = 1. Let Y be the rotation of point F by angle 3pi/4 around point A. Point L is obtained by rotating point A by angle pi/12 about point Y. Line I is the perpendicular bisector of segment LY. Line J is the angle bisector of angle YFL. Line U is the reflection of line J across line I. Line X passes through points A and F. Let M be the perpendicular bisector of segment AL. Point Z is the reflection of point F across line U. Let G be the reflection of point Y across point A. Point D is the reflection of point A across line J. Point V is the reflection of point G across line M. Point C is the reflection of point V across point D. Point H is the reflection of point L across segment YZ. Point N is the reflection of point C across line X. What is the length of segment NH? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
{"messages": [{"content": "Let RX = 5. Let Y be the rotation of point X by angle pi/2 around point R. Point F is obtained by rotating point R by angle pi/3 about point X. Point S is the reflection of point Y across point R. Let T be the vector from point R to point F. Line Q passes through points Y and X. Let G be the reflection of point R across point S. Let A be the reflection of line Q through point S. Point O is the reflection of point F across line A. Let U be point O translated by vector T. Line H passes through points X and G. Let C be the rotation of point S by angle pi/4 around point F. Point W is the reflection of point C across line H. Point D is the reflection of point W across segment YF. Point K is the reflection of point R across segment UD. Find the distance between points O and K. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.59", "dataset": "MATH"}
{"messages": [{"content": "BK = 9. Let Z be the perpendicular bisector of segment KB. Let R be the midpoint of segment KB. Let E be the reflection of point R across point B. Line Y passes through point K parallel to line Z. Point M is obtained by rotating point B by angle 5pi/12 about point K. Point V is the reflection of point B across line Y. Point I is the reflection of point E across point M. Point W is the reflection of point B across segment IM. Point D is the reflection of point V across segment IM. Let L be the midpoint of segment WD. What is the length of segment IL? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.51", "dataset": "MATH"}
{"messages": [{"content": "BQ = 3. Let I be the midpoint of segment QB. Point G is obtained by rotating point B by angle 5pi/12 about point I. Let Z be the midpoint of segment BI. Let D be the angle bisector of angle IBZ. Point J is obtained by rotating point Q by angle 5pi/12 about point I. Line O is the perpendicular bisector of segment JB. Line N is the reflection of line D across line O. Let V be the reflection of point G across point B. Point U is the reflection of point V across line N. Find the length of segment GU. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.65", "dataset": "MATH"}
{"messages": [{"content": "Let YK = 3. Line L is the perpendicular bisector of segment YK. Point M is obtained by rotating point Y by angle pi/2 about point K. Let W be the rotation of point M by angle pi/12 around point Y. Point S is the reflection of point K across point W. Point H is the reflection of point W across line L. Point X is the midpoint of segment SM. Point J is the midpoint of segment XH. What is the distance between points J and M? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.51", "dataset": "MATH"}
{"messages": [{"content": "Let GW = 6. Let N be the vector from point W to point G. Point J is obtained by rotating point W by angle 3pi/4 about point G. Let P be point J translated by vector N. Let L be the midpoint of segment WJ. Line O is the angle bisector of angle JGW. Let R be the reflection of line O through point P. Point Y is the midpoint of segment GP. Line C passes through point P perpendicular to line R. Point T is the reflection of point L across line C. What is the distance between points Y and T? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.0", "dataset": "MATH"}
{"messages": [{"content": "PO = 6. Let K be the reflection of point O across point P. Point Z is obtained by rotating point P by angle 11pi/12 about point K. Let T be the line through points Z and P. Let B be the reflection of line T through point K. Let Y be the reflection of line B across line T. Let C be the reflection of line Y across line B. Point J is the midpoint of segment OZ. Point L is the reflection of point Z across line C. Point S is the reflection of point L across segment OZ. What is the length of segment SJ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.25", "dataset": "MATH"}
{"messages": [{"content": "Let PU = 9. Line R is the perpendicular bisector of segment PU. Let E be the reflection of line R through point U. Let J be the rotation of point U by angle pi around point P. Point G is the reflection of point J across line E. Let N be the reflection of point G across point U. Point Y is the reflection of point J across point G. Let X be the midpoint of segment UN. Find the distance between points Y and X. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85.5", "dataset": "MATH"}
{"messages": [{"content": "FP = 10. Let Z be the rotation of point P by angle pi/3 around point F. Point B is the reflection of point P across point Z. Point S is the midpoint of segment FB. Point W is the midpoint of segment PZ. Let L be the midpoint of segment SP. Let Y be the reflection of point W across point F. Point C is the midpoint of segment BZ. Let V be the reflection of point L across point Z. Point K is the midpoint of segment YV. Point J is the reflection of point C across segment YV. Point E is the midpoint of segment SK. Point Q is the midpoint of segment FJ. Line O passes through point Q perpendicular to segment YV. Point D is the reflection of point F across line O. Find the length of segment ED. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.3", "dataset": "MATH"}
{"messages": [{"content": "Let NR = 9. Let T be the rotation of point N by angle 2pi/3 around point R. Point V is the reflection of point T across segment NR. Line O passes through points V and T. Point Y is the reflection of point N across line O. Line U passes through point Y parallel to line O. Let C be the reflection of line U through point N. Point Z is the reflection of point T across line C. Find the distance between points V and Z. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82.49", "dataset": "MATH"}
{"messages": [{"content": "YX = 12. Let D be the reflection of point X across point Y. Let J be the rotation of point D by angle pi around point X. Let F be the reflection of point Y across point J. Point A is obtained by rotating point F by angle 5pi/6 about point Y. Let O be the rotation of point A by angle pi around point J. Line G passes through points D and O. Point H is the reflection of point Y across line G. Point M is obtained by rotating point H by angle 7pi/12 about point J. Let Z be the angle bisector of angle JAH. Let N be the reflection of line Z through point D. Point E is the reflection of point M across line N. Point L is the reflection of point D across point E. Find the distance between points F and L. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98.66", "dataset": "MATH"}
{"messages": [{"content": "HV = 11. Let R be the rotation of point V by angle pi/2 around point H. Let Z be the rotation of point R by angle pi around point V. Let A be the reflection of point H across point V. Let S be the perpendicular bisector of segment VH. Let C be the reflection of point V across point Z. Point E is the reflection of point R across line S. Line L is the reflection of line S across point E. Point O is the reflection of point A across segment CE. Line P is the reflection of line L across point Z. Point D is the reflection of point C across line P. Point G is the reflection of point O across segment RD. What is the length of segment RG? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.21", "dataset": "MATH"}
{"messages": [{"content": "Let ST = 7. Point F is the midpoint of segment ST. Line R is the perpendicular bisector of segment TF. Point B is the reflection of point S across line R. Let I be the rotation of point B by angle 3pi/4 around point F. Line U is the reflection of line R across point S. Let O be the midpoint of segment BT. Let W be the line through points F and I. Point H is the intersection of lines U and W. What is the length of segment OH? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.51", "dataset": "MATH"}
{"messages": [{"content": "Let MU = 10. Let V be the rotation of point M by angle 2pi/3 around point U. Point S is obtained by rotating point U by angle pi about point V. Let R be the midpoint of segment VU. Let Z be the rotation of point R by angle 11pi/12 around point S. Line H is the perpendicular bisector of segment RS. Line Q passes through point U perpendicular to line H. Point D is the midpoint of segment MS. Point F is the reflection of point D across line Q. Find the distance between points F and Z. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28.21", "dataset": "MATH"}
{"messages": [{"content": "GY = 2. Point Z is the midpoint of segment GY. Point S is obtained by rotating point G by angle pi about point Y. Let D be the perpendicular bisector of segment SY. Line R is the reflection of line D across point Y. Let O be the rotation of point Z by angle 2pi/3 around point S. Let X be the vector from point G to point Y. Let E be the reflection of line R through point O. Let L be the reflection of line E through point S. Let V be point O translated by vector X. Point C is the reflection of point V across line L. Point A is the reflection of point V across line D. Line Q is the angle bisector of angle SCA. Line B is the reflection of line Q across point Z. Let I be the midpoint of segment OZ. Point H is the reflection of point I across line B. What is the distance between points S and H? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.91", "dataset": "MATH"}
{"messages": [{"content": "IC = 3. Let L be the reflection of point C across point I. Let U be the rotation of point L by angle 2pi/3 around point I. Line K is the perpendicular bisector of segment LU. Let D be the midpoint of segment UC. Point E is the reflection of point D across segment IC. Point O is the reflection of point D across line K. What is the distance between points E and O? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.5", "dataset": "MATH"}
{"messages": [{"content": "LO = 9. Let H be the midpoint of segment OL. Point J is the midpoint of segment LH. Let W be the reflection of point O across point L. Point U is the reflection of point O across point W. Point C is the midpoint of segment OJ. Point R is the reflection of point J across point L. Let V be the perpendicular bisector of segment RC. Point Q is the reflection of point U across line V. Let N be the reflection of point W across point Q. What is the distance between points R and N? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72.0", "dataset": "MATH"}
{"messages": [{"content": "QN = 3. Line U passes through points N and Q. Point E is obtained by rotating point N by angle pi/6 about point Q. Point J is the reflection of point E across line U. Point P is obtained by rotating point J by angle 11pi/12 about point N. Line V is the perpendicular bisector of segment JP. Point S is the reflection of point E across point Q. Point K is the reflection of point Q across line V. Point R is the reflection of point K across segment PN. Point I is the reflection of point R across segment SP. Find the distance between points I and J. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.93", "dataset": "MATH"}
{"messages": [{"content": "IC = 3. Point K is the midpoint of segment IC. Let S be the midpoint of segment CK. Point N is obtained by rotating point K by angle pi/6 about point C. Let L be the reflection of point C across point N. Let V be the rotation of point S by angle 3pi/4 around point L. Let M be the reflection of point C across point I. Let Q be the line through point V parallel to segment NM. Point X is the reflection of point S across line Q. Point F is the midpoint of segment NM. Find the distance between points X and F. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.09", "dataset": "MATH"}
{"messages": [{"content": "RK = 2. Line F is the perpendicular bisector of segment KR. Point E is obtained by rotating point R by angle pi/3 about point K. Line Z passes through points E and K. Point Y lies on line Z. Point J is the midpoint of segment YK. Let W be the perpendicular bisector of segment YK. Line U is the reflection of line Z across point R. Let B be the reflection of line W across line F. Lines B and U intersect at point V. Let X be the reflection of point V across point J. What is the length of segment RX? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.21", "dataset": "MATH"}
{"messages": [{"content": "Let VW = 1. Point A is obtained by rotating point W by angle 11pi/12 about point V. Line E is the perpendicular bisector of segment AV. Point Y is obtained by rotating point V by angle 5pi/6 about point A. Line G is the angle bisector of angle YVW. Line L is the reflection of line G across line E. Let Q be the midpoint of segment YW. Point R is the reflection of point Y across line L. What is the distance between points Q and R? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.34", "dataset": "MATH"}
{"messages": [{"content": "Let HM = 11. Let E be the perpendicular bisector of segment HM. Point Z lies on line E at distance 5 from point M. Let P be the reflection of point Z across point H. Let T be the midpoint of segment ZM. Line J passes through points M and Z. Point Q is the reflection of point P across point T. Point D is the reflection of point Q across line J. Find the distance between points Q and D. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29.6", "dataset": "MATH"}
{"messages": [{"content": "Let VG = 5. Line N is the perpendicular bisector of segment VG. Point Z is the reflection of point G across point V. Let I be the rotation of point V by angle pi/2 around point G. Let O be the line through point I perpendicular to line N. Line T is the reflection of line N across point I. Line D is the reflection of line T across point Z. Point M is the reflection of point G across line O. Point R is the midpoint of segment ZI. Point X is the reflection of point R across line D. Point K is the reflection of point M across segment ZI. What is the distance between points K and X? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44.0", "dataset": "MATH"}
{"messages": [{"content": "Let MB = 8. Let A be the rotation of point B by angle pi/12 around point M. Point T is obtained by rotating point A by angle 3pi/4 about point M. Let E be the rotation of point A by angle pi/12 around point M. Let O be the perpendicular bisector of segment TM. Point F is the reflection of point E across line O. Point Z is the reflection of point T across point E. Let I be the reflection of point F across point M. Find the length of segment IZ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.17", "dataset": "MATH"}
{"messages": [{"content": "HZ = 9. Point J is obtained by rotating point Z by angle pi/4 about point H. Let E be the rotation of point Z by angle 11pi/12 around point J. Let T be the line through points H and E. Point W is the reflection of point J across line T. Let A be the line through point W parallel to line T. Let I be the reflection of line T across line A. Point D is the reflection of point E across line A. Point Y is the reflection of point H across line I. What is the distance between points Y and D? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.85", "dataset": "MATH"}
{"messages": [{"content": "ZT = 2. Point B is the reflection of point Z across point T. Let W be the reflection of point Z across point B. Line A is the perpendicular bisector of segment ZB. Point V is the reflection of point W across line A. Point Y is on line A with |YV| = 9. Line H is the perpendicular bisector of segment TY. Point M is on line H. Point U is the reflection of point M across line A. Point Q is the reflection of point U across point V. Find the distance between points M and Q. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.0", "dataset": "MATH"}
{"messages": [{"content": "XZ = 4. Point O is obtained by rotating point X by angle 5pi/6 about point Z. Let V be the midpoint of segment XZ. Point U is obtained by rotating point Z by angle 3pi/4 about point O. Let B be the angle bisector of angle XUZ. Point T is the reflection of point X across point Z. Let E be the reflection of point V across point T. Point M is the reflection of point O across line B. What is the length of segment EM? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.67", "dataset": "MATH"}
{"messages": [{"content": "Let CR = 4. Line M is the perpendicular bisector of segment RC. Point I is obtained by rotating point C by angle 3pi/4 about point R. Point P is the midpoint of segment RI. Line B passes through point I parallel to line M. Point E is obtained by rotating point I by angle 7pi/12 about point P. Let X be the midpoint of segment PC. Point J is the reflection of point X across line B. Point D is the reflection of point E across segment PC. Let N be the midpoint of segment JP. Let Q be the midpoint of segment DE. Find the distance between points N and Q. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.31", "dataset": "MATH"}
{"messages": [{"content": "Let XK = 4. Let R be the line through points X and K. Let G be the line through point X perpendicular to line R. Point J is the reflection of point K across line G. Let B be the reflection of line G through point K. Point N is the reflection of point J across line B. Let F be the midpoint of segment NX. What is the distance between points F and N? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.0", "dataset": "MATH"}
{"messages": [{"content": "Let ZF = 9. Point X is the midpoint of segment ZF. Point Q is the midpoint of segment FX. Point U is the midpoint of segment QX. Let V be the rotation of point F by angle 5pi/12 around point Z. Point E is obtained by rotating point V by angle pi/4 about point U. Point Y is the midpoint of segment XE. Point A is the midpoint of segment YQ. Let N be the midpoint of segment AV. What is the distance between points E and N? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.0", "dataset": "MATH"}
{"messages": [{"content": "Let KL = 6. Point M is obtained by rotating point K by angle pi/4 about point L. Point W is the midpoint of segment LK. Point D is the midpoint of segment MK. Point V is the midpoint of segment WD. Point O is the reflection of point V across segment LK. Let S be the reflection of point L across point O. Find the length of segment SV. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.16", "dataset": "MATH"}
{"messages": [{"content": "RX = 4. Let L be the reflection of point R across point X. Line K is the angle bisector of angle RXL. Point C is obtained by rotating point L by angle pi/12 about point X. Line I passes through point C parallel to line K. Point O is obtained by rotating point L by angle 7pi/12 about point R. Let A be the reflection of point L across point R. Let W be the line through point O parallel to line I. Point U is obtained by rotating point C by angle 7pi/12 about point X. Point S is obtained by rotating point A by angle pi/6 about point U. Point F is the reflection of point S across line K. Let M be the reflection of point F across point C. Line Q passes through point M perpendicular to line W. Point B is the reflection of point U across line Q. What is the length of segment CB? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.5", "dataset": "MATH"}
{"messages": [{"content": "Let FX = 11. Let G be the perpendicular bisector of segment XF. Point V is the reflection of point F across point X. Point O lies on line G at distance 11 from point X. Line B is the perpendicular bisector of segment XV. Point Z is the reflection of point X across point O. Point Q is the reflection of point Z across segment XV. Point E is the reflection of point Z across line G. Point C is the reflection of point Q across line B. Point N is the reflection of point C across segment XV. Point Y is the reflection of point F across point N. Find the length of segment YE. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59.24", "dataset": "MATH"}
{"messages": [{"content": "Let RW = 9. Let Q be the reflection of point W across point R. Point B is the midpoint of segment WR. Point I is the midpoint of segment BW. Point K is the midpoint of segment RB. Let L be the midpoint of segment KQ. What is the distance between points L and I? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.12", "dataset": "MATH"}
{"messages": [{"content": "Let XV = 12. Point K is obtained by rotating point X by angle pi about point V. Let L be the perpendicular bisector of segment KV. Point C lies on line L at distance 7 from point K. Line F passes through point C perpendicular to line L. Point O is the reflection of point C across segment XV. Let Y be the reflection of point O across point C. Point D is the reflection of point V across line F. Find the length of segment YD. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.22", "dataset": "MATH"}
{"messages": [{"content": "WV = 1. Let N be the midpoint of segment WV. Line T is the angle bisector of angle WNV. Point B is on line T with |BN| = 3. Point C is the reflection of point B across segment WV. Let X be the reflection of point B across point C. Point J is the midpoint of segment WX. Point F is the reflection of point J across point V. Find the length of segment FJ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.12", "dataset": "MATH"}
{"messages": [{"content": "BA = 4. Let W be the line through point B perpendicular to segment BA. Point L is obtained by rotating point A by angle 5pi/6 about point B. Line T passes through point L perpendicular to segment BA. Let P be the reflection of line W through point A. Line Q is the angle bisector of angle BLA. Line M is the reflection of line T across line Q. Point V is the reflection of point B across line M. Point E is the reflection of point A across line P. What is the measure of angle VAE, in radians? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.62", "dataset": "MATH"}
{"messages": [{"content": "Let ZL = 10. Point J is obtained by rotating point L by angle 2pi/3 about point Z. Point R is the reflection of point Z across point J. Let Q be the perpendicular bisector of segment ZR. Point O is the reflection of point L across point R. Let W be the reflection of line Q through point O. Point I is the reflection of point O across line W. Point H is the reflection of point L across line Q. Point M is the reflection of point H across segment JZ. Point G is the reflection of point I across point L. Find the distance between points G and M. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "153.95", "dataset": "MATH"}
{"messages": [{"content": "AN = 7. Let P be the midpoint of segment NA. Point F is the midpoint of segment NP. Point K is the midpoint of segment FP. Let V be the line through point A perpendicular to segment PN. Let X be the midpoint of segment KP. Line E is the angle bisector of angle APX. Point R is the reflection of point F across line E. Point O is the reflection of point F across line V. What is the distance between points O and R? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.0", "dataset": "MATH"}
{"messages": [{"content": "GN = 9. Line M is the perpendicular bisector of segment GN. Line V passes through points N and G. Point C lies on line M at distance 9 from point N. Let D be the rotation of point G by angle 7pi/12 around point C. Point T is the reflection of point D across line V. Point S is the reflection of point T across line M. Point P is the reflection of point C across segment DS. What is the length of segment DP? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.06", "dataset": "MATH"}
{"messages": [{"content": "QN = 9. Point Y is the midpoint of segment NQ. Let Z be the rotation of point Q by angle pi/3 around point Y. Line M passes through point Q parallel to segment ZY. Let W be the reflection of point N across point Z. Point D is the reflection of point Y across point W. Let O be the rotation of point W by angle pi around point Y. Point I is the midpoint of segment OZ. Line J passes through point D parallel to line M. Point F is the reflection of point O across line J. Point X is the midpoint of segment DI. What is the length of segment XF? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26.6", "dataset": "MATH"}
{"messages": [{"content": "Let VY = 9. Point P is the reflection of point Y across point V. Point J is obtained by rotating point P by angle 11pi/12 about point Y. Let W be the perpendicular bisector of segment JP. Point X is obtained by rotating point V by angle 3pi/4 about point J. Let F be the line through points J and Y. Let C be the reflection of line W across line F. Let L be the reflection of line W through point V. Point B is the reflection of point Y across line L. Point Q is the reflection of point X across line C. Find the distance between points Q and B. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.6", "dataset": "MATH"}
{"messages": [{"content": "VC = 6. Point T is the midpoint of segment VC. Point E is the midpoint of segment TV. Point D is the reflection of point E across point C. Point R is the reflection of point C across point V. Let X be the midpoint of segment ET. Point B is the reflection of point D across point R. What is the distance between points B and X? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.75", "dataset": "MATH"}
{"messages": [{"content": "Let ZS = 7. Let N be the vector from point Z to point S. Let D be the midpoint of segment ZS. Let F be the angle bisector of angle SDZ. Line T is the reflection of line F across point S. Line W is the reflection of line F across point Z. Point L lies on line T at distance 9 from point Z. Let M be the angle bisector of angle SLD. Let Y be the line through point S parallel to line M. Point B is the midpoint of segment ZL. Let K be point L translated by vector N. Let P be point B translated by vector N. Let Q be the line through point P perpendicular to line Y. Point H is the reflection of point B across line Q. Point U is the midpoint of segment ZH. Point A is the reflection of point K across point U. Point C is the reflection of point A across line W. What is the length of segment CZ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.38", "dataset": "MATH"}
{"messages": [{"content": "KD = 10. Let N be the rotation of point K by angle 5pi/6 around point D. Let F be the rotation of point K by angle pi/4 around point D. Point X is the reflection of point N across point D. Point V is the midpoint of segment FX. Point E is the midpoint of segment XD. Line Q passes through point F perpendicular to segment FX. Let T be the midpoint of segment EV. Point O is the reflection of point V across line Q. Point S is the midpoint of segment FT. What is the length of segment SO? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.94", "dataset": "MATH"}
{"messages": [{"content": "IC = 2. Point P is the midpoint of segment CI. Line F passes through points P and C. Let Z be the line through point P perpendicular to line F. Point A is on line F with |AI| = 5. Let K be the vector from point I to point A. Line L passes through point I parallel to line Z. Point X is on line L with |XP| = 3. Point Y is the translation of point X by vector K. Point G is on line L with |GX| = 10. Line O passes through point G perpendicular to line Z. Let V be the line through points G and Y. Point W is the intersection of lines F and V. Let Q be the reflection of line O through point P. Point E is the reflection of point X across point W. Point B is the reflection of point E across line Q. Find the length of segment BE. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.0", "dataset": "MATH"}
{"messages": [{"content": "Let BQ = 8. Line K passes through points B and Q. Point A is the midpoint of segment BQ. Point N lies on line K at distance 9 from point B. Point X is on line K. Let V be the rotation of point N by angle pi/3 around point X. Let M be the midpoint of segment VB. Let T be the midpoint of segment AV. Point Y is the reflection of point M across segment AV. Find the distance between points Y and T. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "JT = 9. Point D is obtained by rotating point T by angle pi/12 about point J. Let R be the vector from point J to point T. Let N be point T translated by vector R. Point H is the midpoint of segment JD. Point M is the midpoint of segment HD. Point C is the midpoint of segment HN. Let K be the reflection of point M across point C. What is the distance between points H and K? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.61", "dataset": "MATH"}
{"messages": [{"content": "UK = 11. Let H be the midpoint of segment UK. Let A be the rotation of point H by angle pi/3 around point U. Let X be the vector from point U to point A. Point O is the reflection of point K across point U. Let D be point H translated by vector X. Let G be the line through points U and D. Point J is obtained by rotating point A by angle pi about point U. Line Q is the reflection of line G across point K. Point S is the reflection of point J across segment AO. Segments SH and AO intersect at point E. Point B is the reflection of point S across line Q. Find the distance between points B and E. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36.91", "dataset": "MATH"}
{"messages": [{"content": "Let TZ = 9. Point I is obtained by rotating point T by angle pi/6 about point Z. Let D be the midpoint of segment ZT. Let H be the rotation of point D by angle pi/4 around point Z. Let K be the midpoint of segment DI. Let R be the midpoint of segment TI. Line P is the perpendicular bisector of segment KD. Point F is the reflection of point H across line P. Let E be the reflection of point R across point F. Find the distance between points T and E. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.3", "dataset": "MATH"}
{"messages": [{"content": "Let GZ = 8. Let J be the midpoint of segment GZ. Let D be the angle bisector of angle JZG. W is placed 9 units away from Z. Let L be the angle bisector of angle GJW. Point K lies on line L at distance 4 from point J. Point P is the reflection of point K across line D. Point A is the reflection of point J across segment GW. Point H is the reflection of point P across segment GW. What is the distance between points H and A? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Let PF = 3. Point K is the reflection of point P across point F. Point V is obtained by rotating point K by angle 7pi/12 about point P. Point E is obtained by rotating point K by angle 11pi/12 about point P. Let O be the perpendicular bisector of segment EV. Let N be the reflection of line O through point K. Let X be the midpoint of segment KE. Point C is the reflection of point X across line N. What is the distance between points C and V? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.16", "dataset": "MATH"}
{"messages": [{"content": "Let RE = 6. Point I is the midpoint of segment ER. Let L be the midpoint of segment RI. Line J is the perpendicular bisector of segment LE. Let D be the midpoint of segment RL. Point C is the midpoint of segment LD. Let S be the reflection of point C across point D. Point O is the midpoint of segment RC. Let K be the rotation of point L by angle 5pi/6 around point C. Point M is the midpoint of segment KE. Point U is the reflection of point O across line J. Let N be the midpoint of segment SM. Point W is the reflection of point N across segment CM. Point A is the reflection of point U across segment CM. Find the distance between points A and W. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.05", "dataset": "MATH"}
{"messages": [{"content": "XK = 6. Let W be the rotation of point X by angle pi/2 around point K. Let A be the midpoint of segment XK. Point Z is the reflection of point A across point K. Point I is the reflection of point K across point W. Let S be the reflection of point K across point Z. Find the distance between points I and S. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.42", "dataset": "MATH"}
{"messages": [{"content": "Let WE = 6. Let S be the rotation of point E by angle 5pi/12 around point W. Line G passes through point S perpendicular to segment SW. Let C be the line through point E parallel to line G. Let P be the reflection of point W across point S. Point Q is the midpoint of segment SE. Point J is the reflection of point E across segment QP. Let B be the line through point W parallel to segment QP. Lines B and C intersect at point A. Let M be the midpoint of segment JP. What is the distance between points M and A? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.82", "dataset": "MATH"}
{"messages": [{"content": "Let AJ = 5. Let H be the rotation of point A by angle 5pi/12 around point J. Let Q be the reflection of point J across point H. Let I be the line through point H parallel to segment AQ. Let K be the perpendicular bisector of segment AQ. Point S is the reflection of point J across line I. Let R be the reflection of point S across point Q. Point V is the reflection of point R across line K. Point T is the midpoint of segment VQ. Let B be the midpoint of segment HQ. Find the length of segment TB. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.27", "dataset": "MATH"}
{"messages": [{"content": "Let NB = 1. Point Y is the midpoint of segment NB. Let V be the reflection of point B across point N. Line Q is the perpendicular bisector of segment YV. Point I is the reflection of point B across line Q. Point F is the midpoint of segment VI. What is the distance between points N and F? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.25", "dataset": "MATH"}
{"messages": [{"content": "EG = 4. Let O be the midpoint of segment GE. Let Q be the rotation of point G by angle 5pi/12 around point E. Let B be the rotation of point E by angle pi around point Q. Let D be the midpoint of segment QE. Let S be the perpendicular bisector of segment GO. Point P lies on line S. Line M passes through point P parallel to segment QB. Let R be the line through point Q perpendicular to line M. Point X is the reflection of point G across point E. Point F is the reflection of point D across line R. Find the length of segment XF. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.03", "dataset": "MATH"}
{"messages": [{"content": "Let IK = 8. Point J is obtained by rotating point K by angle pi/3 about point I. Point E is obtained by rotating point J by angle pi about point I. Line B is the perpendicular bisector of segment IE. Point G is on line B with |GJ| = 12. Point Q is the reflection of point G across segment IE. Point R is the midpoint of segment QK. Let C be the midpoint of segment JQ. Find the length of segment RC. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "EA = 3. Let S be the perpendicular bisector of segment AE. Line I is the reflection of line S across point E. Point D lies on line I. Line Y is the reflection of line S across point D. Point H is the reflection of point D across line Y. Find the distance between points H and D. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.0", "dataset": "MATH"}
{"messages": [{"content": "RS = 2. Point E is the reflection of point R across point S. Point Q is the reflection of point S across point R. Let Y be the angle bisector of angle SRQ. Let H be the angle bisector of angle ESQ. Let Z be the reflection of line Y through point Q. Let X be the midpoint of segment QE. Line K passes through point Q parallel to line H. Point P is the reflection of point X across line Z. Point C lies on line K at distance 1 from point S. Point F is the reflection of point S across point E. Point D is the midpoint of segment CF. Point N is the midpoint of segment PD. Find the distance between points P and N. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.51", "dataset": "MATH"}
{"messages": [{"content": "Let BW = 10. Let T be the rotation of point W by angle pi/4 around point B. Point Q is the reflection of point W across point T. Line N passes through points Q and B. Line P passes through point T perpendicular to line N. Point R is the reflection of point Q across line P. Find the length of segment RT. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.65", "dataset": "MATH"}
{"messages": [{"content": "AK = 12. Point D is the midpoint of segment KA. Line W is the perpendicular bisector of segment KD. Point R is the reflection of point A across line W. Let S be the rotation of point D by angle 2pi/3 around point R. Let H be the angle bisector of angle RSA. Line O passes through point A perpendicular to line H. Point X is the reflection of point R across point S. Line G is the reflection of line O across point D. Point M is the intersection of line G and segment XA. What is the distance between points A and M? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.03", "dataset": "MATH"}
{"messages": [{"content": "Let LK = 10. Point A is obtained by rotating point L by angle 2pi/3 about point K. Line B is the perpendicular bisector of segment LK. Let S be the midpoint of segment LA. Let M be the reflection of point S across point A. Point P is the reflection of point A across line B. Point R is the reflection of point P across segment LA. Let D be the midpoint of segment MP. Point Y is the reflection of point R across segment PD. What is the distance between points L and Y? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28.23", "dataset": "MATH"}
{"messages": [{"content": "NF = 11. Let W be the line through point N perpendicular to segment NF. Line H is the perpendicular bisector of segment NF. Point Y is on line W with |YF| = 1. Let V be the midpoint of segment NF. Line E is the reflection of line W across line H. Point D is the midpoint of segment VF. Line A passes through point D parallel to line E. Point Z is the reflection of point Y across line A. Find the distance between points Z and D. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.31", "dataset": "MATH"}
{"messages": [{"content": "NS = 6. Let G be the rotation of point N by angle pi/12 around point S. Let P be the midpoint of segment NS. Point D is the reflection of point G across segment NS. Let X be the rotation of point N by angle 3pi/4 around point D. Let R be the line through point X perpendicular to segment NS. Let J be the reflection of point X across point P. Point W is the reflection of point D across line R. Point H is the midpoint of segment GJ. What is the length of segment HW? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.6", "dataset": "MATH"}
{"messages": [{"content": "Let NJ = 8. Point L is obtained by rotating point J by angle pi/2 about point N. Point Y is the reflection of point J across point N. Line M is the perpendicular bisector of segment YJ. Let T be the reflection of point N across point J. Point V lies on line M. Point W lies on line M at distance 12 from point T. Let K be the reflection of point W across point V. Point Z is the midpoint of segment YK. Line C passes through points L and Z. Point X is the reflection of point V across line C. Find the length of segment ZX. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.21", "dataset": "MATH"}
{"messages": [{"content": "IK = 1. B is placed 1 units away from K. Point U is obtained by rotating point B by angle 7pi/12 about point K. Let L be the rotation of point B by angle 3pi/4 around point K. Point M is obtained by rotating point U by angle 7pi/12 about point L. Point W is the midpoint of segment MK. Let Z be the line through points W and U. Point E is the reflection of point B across line Z. What is the distance between points M and E? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
{"messages": [{"content": "JR = 1. Line Z is the perpendicular bisector of segment JR. Let E be the vector from point J to point R. Point K is the midpoint of segment RJ. Let T be point R translated by vector E. Let I be the line through point J parallel to line Z. Let N be the perpendicular bisector of segment KT. Let F be the rotation of point T by angle 3pi/4 around point R. Let D be the line through point T parallel to line I. Let B be the line through point F parallel to line D. Point U is the reflection of point J across line B. Point L is the reflection of point U across line N. Point A is the reflection of point F across point L. Point X is the reflection of point J across point U. Find the length of segment XA. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.47", "dataset": "MATH"}
{"messages": [{"content": "LV = 6. Let R be the reflection of point L across point V. Let N be the reflection of point V across point L. Let X be the rotation of point L by angle pi around point R. Line J is the perpendicular bisector of segment LN. Point H is the midpoint of segment VX. Let Z be the reflection of point L across point N. Point D lies on line J at distance 4 from point R. Line G passes through point R parallel to segment DZ. Let P be the line through point N perpendicular to segment NL. Line F passes through point Z perpendicular to segment NL. Line O is the reflection of line F across line P. Point U is the intersection of lines O and G. Find the distance between points H and U. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.92", "dataset": "MATH"}
{"messages": [{"content": "KM = 8. Point A is the midpoint of segment KM. Point C is the reflection of point A across point K. Point R is the reflection of point C across point A. Point O is obtained by rotating point A by angle pi/4 about point M. Let Z be the rotation of point C by angle 7pi/12 around point A. Let G be the rotation of point O by angle 11pi/12 around point A. Line D is the perpendicular bisector of segment KC. Point J is the midpoint of segment GZ. Point H is the reflection of point J across line D. Point W is the reflection of point H across segment KM. What is the distance between points R and W? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.97", "dataset": "MATH"}
{"messages": [{"content": "Let BM = 1. Point P is the midpoint of segment MB. Point F is obtained by rotating point B by angle 3pi/4 about point M. Let H be the rotation of point P by angle pi/12 around point M. Let K be the perpendicular bisector of segment FB. Point L is the reflection of point H across line K. Point Y is the reflection of point H across segment BL. What is the distance between points L and Y? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.79", "dataset": "MATH"}
{"messages": [{"content": "Let GX = 10. Let O be the perpendicular bisector of segment GX. J is constructed so that XJ = 9. Let S be the midpoint of segment JX. Let K be the line through points S and G. Let P be the reflection of point G across point S. Line V is the reflection of line O across line K. Line Y passes through point P parallel to line V. Point W is the reflection of point J across line Y. What is the distance between points P and W? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.0", "dataset": "MATH"}
{"messages": [{"content": "NJ = 2. Let Q be the perpendicular bisector of segment JN. Line I is the reflection of line Q across point N. Point C is the reflection of point J across point N. Let D be the vector from point C to point J. Let R be point J translated by vector D. Let W be the reflection of line I across line Q. Let M be the reflection of line W across line I. Point K is the reflection of point N across line M. Let L be the midpoint of segment JR. Let H be the line through point L perpendicular to segment JC. Point T is the reflection of point K across line H. What is the distance between points T and L? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.0", "dataset": "MATH"}
{"messages": [{"content": "Let MS = 11. Point P is obtained by rotating point S by angle 5pi/6 about point M. Let V be the line through points P and M. Let I be the midpoint of segment SM. Let O be the midpoint of segment SI. Let N be the angle bisector of angle MPI. Line A is the reflection of line N across point I. Point C is the intersection of lines V and A. What is the distance between points C and O? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50.32", "dataset": "MATH"}
{"messages": [{"content": "Let WH = 1. Line T is the perpendicular bisector of segment HW. Point K is the midpoint of segment WH. Point I is obtained by rotating point W by angle pi/12 about point K. Line E passes through points I and H. Line C is the reflection of line E across point K. Point M is the reflection of point H across line C. Point D lies on line T. Line L passes through points D and M. Point P is the reflection of point W across line L. Find the length of segment PM. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "PB = 6. Let N be the perpendicular bisector of segment BP. Point I lies on line N at distance 1 from point P. Point A lies on line N at distance 4 from point B. Let K be the midpoint of segment BA. Let L be the midpoint of segment AI. Line M passes through point L perpendicular to line N. Point S is the reflection of point K across line M. What is the distance between points S and K? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Let VG = 2. Line C is the perpendicular bisector of segment VG. Let O be the midpoint of segment GV. Line X is the reflection of line C across point G. Point Z is obtained by rotating point V by angle 11pi/12 about point G. Let T be the reflection of line X across line C. Line P is the reflection of line C across line T. Point D is the reflection of point G across point V. Point Y lies on line P at distance 2 from point O. Let R be the perpendicular bisector of segment ZD. Point Q lies on line R. Point A is the midpoint of segment YQ. Let M be the midpoint of segment AQ. Point I is the reflection of point D across segment MO. Find the distance between points I and O. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "BA = 3. Point D is obtained by rotating point B by angle 2pi/3 about point A. Let K be the perpendicular bisector of segment AB. Let E be the line through points B and A. Let V be the reflection of line K through point D. Lines E and V intersect at point Z. What is the distance between points B and Z? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.5", "dataset": "MATH"}
{"messages": [{"content": "Let ET = 6. Point C is obtained by rotating point E by angle 11pi/12 about point T. Line V is the perpendicular bisector of segment EC. Let S be the reflection of line V through point E. Let O be the reflection of point E across point T. Point G is the reflection of point O across line S. Point P is the reflection of point E across point C. Let F be the midpoint of segment TG. Find the length of segment FP. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32.74", "dataset": "MATH"}
{"messages": [{"content": "Let CV = 5. Let L be the midpoint of segment CV. Let J be the midpoint of segment VL. Let A be the rotation of point L by angle 3pi/4 around point V. Point T is the reflection of point C across point A. Point B is obtained by rotating point J by angle 5pi/6 about point C. Let E be the rotation of point T by angle pi/3 around point B. Let X be the reflection of point C across point B. Let H be the angle bisector of angle AXE. Let Q be the midpoint of segment XJ. Point Z is the reflection of point Q across line H. What is the distance between points Z and T? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.2", "dataset": "MATH"}
{"messages": [{"content": "Let HI = 9. Let M be the reflection of point I across point H. Let C be the reflection of point I across point M. Point K is the reflection of point H across point C. Let V be the vector from point H to point I. Point N is obtained by rotating point M by angle 3pi/4 about point K. Let U be point N translated by vector V. Line T is the angle bisector of angle UNI. Let Q be the line through point C perpendicular to line T. Point O is the reflection of point C across line T. Point S is the reflection of point C across point O. Point R is the reflection of point I across line Q. Point X is the midpoint of segment OR. Find the length of segment XS. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65.33", "dataset": "MATH"}
{"messages": [{"content": "JW = 10. Point H is the reflection of point W across point J. Let L be the reflection of point W across point H. Let S be the line through points L and J. Line M passes through point H perpendicular to line S. Let N be the rotation of point J by angle 3pi/4 around point L. Let Z be the reflection of line M through point W. Let F be the reflection of line M across line Z. Line B is the reflection of line M across line F. Point Y is the reflection of point N across line B. Point P lies on line F. Point K is the midpoint of segment YP. Point C is the reflection of point H across segment YK. Find the distance between points Y and C. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "361.84", "dataset": "MATH"}
{"messages": [{"content": "AC = 1. Let N be the reflection of point A across point C. Point I is the reflection of point N across point A. Point D is the midpoint of segment AI. Let W be the rotation of point A by angle 3pi/4 around point D. Let X be the rotation of point W by angle 7pi/12 around point N. Let L be the midpoint of segment DX. Point B is the midpoint of segment IX. Find the distance between points B and L. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "IE = 4. Point A is obtained by rotating point I by angle 11pi/12 about point E. Let P be the midpoint of segment EA. Let K be the angle bisector of angle PAI. Line W passes through point I parallel to line K. Point B is the reflection of point P across line W. Let D be the midpoint of segment IP. Let N be the reflection of point D across point A. Point T is the reflection of point E across line W. Point J is the reflection of point T across segment IA. Let R be the reflection of point J across point N. Point S is the midpoint of segment BA. What is the distance between points S and R? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.04", "dataset": "MATH"}
{"messages": [{"content": "Let EO = 3. Let H be the rotation of point O by angle 5pi/6 around point E. Let J be the rotation of point O by angle 3pi/4 around point H. Let F be the vector from point H to point O. Let S be point E translated by vector F. Let X be the rotation of point S by angle 5pi/6 around point J. Line Y is the angle bisector of angle HSE. Point N is the reflection of point X across line Y. Point M is the reflection of point J across line Y. Let B be the perpendicular bisector of segment JO. Point W is the midpoint of segment EO. Let Z be the reflection of point W across point N. Point U is the reflection of point Z across line B. What is the length of segment UM? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39.09", "dataset": "MATH"}
{"messages": [{"content": "FS = 9. Point V is the midpoint of segment SF. Let C be the perpendicular bisector of segment SV. Line Y is the reflection of line C across point S. Point O is the reflection of point F across line Y. Find the distance between points O and V. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.0", "dataset": "MATH"}
{"messages": [{"content": "SN = 6. Let P be the vector from point S to point N. Let A be point N translated by vector P. Point Y is obtained by rotating point N by angle 5pi/12 about point A. Let W be the reflection of point N across point S. Point R is the midpoint of segment AY. Let O be the midpoint of segment AR. Line F is the perpendicular bisector of segment AY. Let V be the line through points W and R. Line Z is the reflection of line V across line F. Segment SN and line Z intersect at point K. What is the length of segment OK? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.29", "dataset": "MATH"}
{"messages": [{"content": "OK = 9. Point X is the reflection of point K across point O. Point Q is obtained by rotating point X by angle pi/6 about point O. Let M be the perpendicular bisector of segment XQ. Line S passes through point O perpendicular to line M. Point N is the midpoint of segment OK. Let I be the line through point N perpendicular to line S. Point F is on line I. Point R is the midpoint of segment FQ. Point P is the reflection of point X across point R. Find the distance between points F and P. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.66", "dataset": "MATH"}
{"messages": [{"content": "OT = 1. Point E is the midpoint of segment TO. Let H be the vector from point E to point O. Point A is the midpoint of segment OE. Line F is the perpendicular bisector of segment TO. Line C is the reflection of line F across point O. Point W is the midpoint of segment TE. Let I be the reflection of line F across line C. Let Q be point O translated by vector H. Let R be the rotation of point E by angle pi around point T. Point B is the reflection of point Q across point W. Line S is the perpendicular bisector of segment QO. Line J is the reflection of line S across line C. Line V passes through point B parallel to line I. Let G be the reflection of line J across line V. Point L is the reflection of point A across line G. What is the distance between points R and L? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.75", "dataset": "MATH"}
{"messages": [{"content": "XQ = 7. Point P is the reflection of point Q across point X. Let R be the rotation of point X by angle 5pi/12 around point P. Point U is the midpoint of segment QR. Line B is the perpendicular bisector of segment QX. Line F is the reflection of line B across point X. Let V be the perpendicular bisector of segment UQ. Let I be the reflection of line V across line B. Point M is the reflection of point U across segment QX. Point Z is the intersection of lines F and I. What is the length of segment ZM? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.44", "dataset": "MATH"}
{"messages": [{"content": "MW = 4. Let N be the rotation of point W by angle pi/6 around point M. Let U be the line through points M and N. Let F be the rotation of point M by angle pi/3 around point W. Line D passes through points M and W. Line A is the reflection of line U across line D. Let O be the reflection of point F across point M. Point P is obtained by rotating point F by angle pi/12 about point O. Line J passes through points F and P. Point T is the intersection of lines J and A. Line S is the reflection of line U across point T. Lines J and S intersect at point R. Find the distance between points F and R. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26.32", "dataset": "MATH"}
{"messages": [{"content": "Let OM = 9. Let X be the reflection of point M across point O. Let F be the line through points M and X. Point N is on line F. Let J be the rotation of point O by angle 7pi/12 around point X. Let Q be the reflection of point M across point N. Point W is the reflection of point Q across point J. Point Z is the midpoint of segment WJ. Line K passes through point Z perpendicular to line F. Point R is the reflection of point O across line K. What is the distance between points R and W? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.75", "dataset": "MATH"}
{"messages": [{"content": "YU = 6. Let S be the line through points U and Y. Let X be the rotation of point U by angle pi/4 around point Y. Line W is the perpendicular bisector of segment YX. Line T is the reflection of line W across point Y. Let D be the line through point U perpendicular to line S. Line I is the reflection of line T across line S. Let V be the line through point X perpendicular to line T. Let E be the midpoint of segment XY. Let N be the midpoint of segment EU. Line B passes through point N parallel to line D. Line L passes through point N parallel to line S. Point Z is the reflection of point N across line I. Let H be the reflection of line L across line V. Let F be the rotation of point Y by angle pi/2 around point Z. Let G be the rotation of point F by angle 7pi/12 around point U. Segment FG and line H intersect at point R. Let M be the reflection of point E across point R. Point K is the intersection of lines T and B. Point J is the reflection of point K across segment GX. Point P is the reflection of point M across segment FG. Find the length of segment JP. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.6", "dataset": "MATH"}
{"messages": [{"content": "Let GQ = 1. Let O be the vector from point Q to point G. Let J be the line through points G and Q. Let R be the midpoint of segment QG. Let S be point R translated by vector O. Let L be the perpendicular bisector of segment QG. Point Z is obtained by rotating point R by angle 2pi/3 about point G. Let U be the reflection of point G across point Z. Let F be the reflection of point Q across point U. Point Y is obtained by rotating point Z by angle 5pi/6 about point U. Let K be the midpoint of segment YS. Point D is the reflection of point Z across line L. Point W is the midpoint of segment UQ. Line E passes through point F parallel to line J. Line M passes through points D and W. Line M and segment GK intersect at point C. Point V is the reflection of point K across line M. Let X be the reflection of point G across point C. Let P be the line through point X perpendicular to line E. Point T is the reflection of point V across line P. What is the length of segment ZT? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
{"messages": [{"content": "Let ZP = 5. Let C be the midpoint of segment ZP. Line F passes through point P perpendicular to segment ZP. Point M is obtained by rotating point C by angle pi/6 about point P. Point N is the reflection of point C across point Z. Point L is the reflection of point Z across line F. Line Q passes through point N parallel to line F. Line A is the reflection of line Q across line F. Point D is the reflection of point L across line A. Find the length of segment DM. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.23", "dataset": "MATH"}
{"messages": [{"content": "Let TY = 1. Line A passes through points Y and T. Point V is the reflection of point T across point Y. Line U passes through point T perpendicular to line A. Point K is the reflection of point Y across line U. Find the distance between points V and K. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Let KH = 9. Point A is obtained by rotating point H by angle 11pi/12 about point K. Point L is the reflection of point K across point A. Point S is obtained by rotating point L by angle pi/12 about point K. Let M be the rotation of point K by angle pi/6 around point S. Let V be the reflection of point A across point M. Let Z be the reflection of point V across point L. Line J passes through point Z perpendicular to segment KS. Point W is the reflection of point Z across segment KS. Point N is the reflection of point A across line J. Let E be the midpoint of segment NW. Find the distance between points K and E. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53.79", "dataset": "MATH"}
{"messages": [{"content": "IU = 12. Let T be the midpoint of segment UI. Line Z passes through points U and T. Let F be the rotation of point U by angle 2pi/3 around point I. Let P be the midpoint of segment IT. Point E is on line Z with |EP| = 2. Point Y is the reflection of point T across point I. Line O is the perpendicular bisector of segment YE. Line X passes through point P parallel to line O. Line K is the reflection of line X across point Y. Point J is the intersection of lines Z and K. What is the length of segment FJ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.75", "dataset": "MATH"}
{"messages": [{"content": "Let LO = 6. Let S be the reflection of point L across point O. Point R is the midpoint of segment OL. Line X is the perpendicular bisector of segment SO. Point A is on line X with |AO| = 9. Line M passes through points A and R. Line U passes through point R perpendicular to line M. Let B be the midpoint of segment OR. Point E is the reflection of point L across line U. Point V is the reflection of point B across line U. What is the length of segment VE? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.5", "dataset": "MATH"}
{"messages": [{"content": "OV = 10. Let G be the reflection of point V across point O. Point T is obtained by rotating point O by angle 2pi/3 about point G. Line U is the angle bisector of angle GTV. Point Q is the reflection of point T across point G. Line X is the reflection of line U across point Q. Point W is the reflection of point V across point Q. Point Z is the reflection of point V across line X. Let A be the reflection of point W across point O. Point D is the reflection of point A across line U. What is the length of segment ZD? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.87", "dataset": "MATH"}
{"messages": [{"content": "Let XP = 6. Let Y be the perpendicular bisector of segment XP. Point W is obtained by rotating point P by angle 7pi/12 about point X. Let G be the reflection of line Y through point P. Let Z be the reflection of point X across point W. Point E is the midpoint of segment PW. Point R is the reflection of point Z across line G. Let S be the angle bisector of angle PZR. Point O is the reflection of point E across line S. Find the length of segment OZ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.2", "dataset": "MATH"}
{"messages": [{"content": "Let CF = 5. Point U is the reflection of point C across point F. Let J be the perpendicular bisector of segment CF. Point W is the reflection of point U across point C. Point X is on line J with |XU| = 12. Let Y be the line through points C and X. Point G is the reflection of point U across line Y. Point T is the reflection of point U across segment XW. What is the distance between points T and G? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.99", "dataset": "MATH"}
{"messages": [{"content": "Let HO = 3. Point K is obtained by rotating point H by angle pi/12 about point O. Point Z is the reflection of point H across segment OK. Let F be the rotation of point O by angle pi/12 around point K. Let L be the angle bisector of angle ZKO. Let Y be the midpoint of segment ZH. Let P be the reflection of line L through point Z. Let R be the line through points H and Y. Lines R and P intersect at point J. Point N is the midpoint of segment ZF. What is the distance between points N and J? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.02", "dataset": "MATH"}
{"messages": [{"content": "Let BL = 8. Point I is the reflection of point B across point L. Let X be the angle bisector of angle ILB. Line W is the perpendicular bisector of segment LB. Point F is the midpoint of segment IL. Point H is obtained by rotating point B by angle 2pi/3 about point L. Let Q be the line through point I parallel to line W. Line N is the reflection of line X across line Q. Point D is the reflection of point F across point I. Point O is the reflection of point L across line N. Point P is obtained by rotating point D by angle pi about point L. Point T is the midpoint of segment OL. Point V is the reflection of point D across point H. Let G be the midpoint of segment TV. Point E is the reflection of point V across line Q. Point Y is the reflection of point E across point I. Point C is the reflection of point Y across point G. Find the distance between points P and C. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39.4", "dataset": "MATH"}
{"messages": [{"content": "EB = 10. Let Z be the vector from point E to point B. Let F be the vector from point B to point E. Line T passes through points B and E. Let V be the vector from point E to point B. Point U is the reflection of point E across point B. Let Y be the rotation of point U by angle 5pi/12 around point B. Point G is the reflection of point Y across line T. Let K be the line through points E and Y. Line A is the reflection of line K across line T. Point W is the translation of point U by vector Z. Let R be the reflection of point Y across point W. Point J is the midpoint of segment GR. Let M be point R translated by vector F. Let N be point J translated by vector V. Let P be point R translated by vector Z. Point Q is the reflection of point P across line A. Let H be the midpoint of segment UW. Let I be the midpoint of segment QN. Let C be the reflection of point M across point I. What is the length of segment HC? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52.99", "dataset": "MATH"}
{"messages": [{"content": "RZ = 7. Let K be the reflection of point R across point Z. Point J is the reflection of point Z across point R. Point W is the midpoint of segment JK. Let A be the rotation of point J by angle pi/12 around point Z. Point D is the midpoint of segment RJ. Point G is obtained by rotating point D by angle pi/3 about point W. Line T is the perpendicular bisector of segment GW. Point B is the midpoint of segment DK. Point L is the reflection of point B across point A. Point O is the reflection of point L across line T. What is the distance between points O and L? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.35", "dataset": "MATH"}
{"messages": [{"content": "RE = 12. Let V be the vector from point E to point R. Let J be the perpendicular bisector of segment RE. Point F is the translation of point R by vector V. Point A is the reflection of point E across point F. Point H is the reflection of point A across point E. Point W is on line J. Line K passes through point W perpendicular to line J. Let B be the line through point F perpendicular to line K. Point T lies on line B. Point U is the reflection of point T across segment AF. Point I is the reflection of point U across point H. What is the distance between points I and T? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "144.0", "dataset": "MATH"}
{"messages": [{"content": "Let QR = 8. Let Y be the rotation of point Q by angle 5pi/12 around point R. Let B be the rotation of point R by angle 3pi/4 around point Y. Line M passes through points B and Y. Point O is the reflection of point R across point Q. Point J is obtained by rotating point R by angle pi/3 about point B. Let F be the reflection of line M through point J. Let N be the line through point R parallel to line F. Let Z be the reflection of point Q across point B. Line C is the reflection of line N across point B. Segment RZ and line C intersect at point H. What is the length of segment OH? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.35", "dataset": "MATH"}
{"messages": [{"content": "Let TJ = 7. Point L is obtained by rotating point J by angle 5pi/12 about point T. Point K is the reflection of point J across point T. Line U passes through point K perpendicular to segment LT. Line N is the reflection of line U across point J. Let D be the reflection of point T across point L. Point Y is obtained by rotating point K by angle 11pi/12 about point T. Line A passes through point T parallel to line N. Line M is the angle bisector of angle DTJ. Point V is obtained by rotating point L by angle pi/2 about point Y. Point W is the reflection of point K across point D. Point P is the midpoint of segment TL. Let F be the reflection of point V across point W. Let X be the line through point F parallel to line A. Point R is the reflection of point P across line M. Point O is the reflection of point J across line X. What is the length of segment RO? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "130.57", "dataset": "MATH"}
{"messages": [{"content": "Let JP = 7. Let V be the rotation of point J by angle pi/6 around point P. Point A is the midpoint of segment PV. Line N is the angle bisector of angle VAJ. Let H be the line through point V parallel to line N. Point L is the reflection of point A across line H. Point O is the reflection of point P across point L. Find the length of segment OJ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.91", "dataset": "MATH"}
{"messages": [{"content": "Let ZN = 10. Point S is the reflection of point N across point Z. Point C is the midpoint of segment ZS. Line Y is the perpendicular bisector of segment CN. Point X is obtained by rotating point C by angle pi/2 about point N. Point M is obtained by rotating point S by angle 3pi/4 about point Z. Line A is the reflection of line Y across point Z. Point H is the reflection of point X across point C. Point L is the reflection of point M across line A. Point F is the reflection of point X across point H. Point K is the midpoint of segment HF. What is the distance between points L and K? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43.59", "dataset": "MATH"}
{"messages": [{"content": "Let TD = 12. Let Q be the perpendicular bisector of segment DT. Let K be the reflection of point T across point D. Let F be the rotation of point T by angle pi around point K. Let R be the midpoint of segment DF. Line S is the reflection of line Q across point T. Line M passes through points R and D. Let J be the rotation of point F by angle 7pi/12 around point R. Line O is the perpendicular bisector of segment DR. Let L be the midpoint of segment JD. Point A lies on line O. Let C be the reflection of line Q through point A. Lines C and M intersect at point Y. Point Z is the reflection of point L across line S. What is the length of segment YZ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67.23", "dataset": "MATH"}
{"messages": [{"content": "Let OD = 11. Point H is obtained by rotating point O by angle pi/3 about point D. Let V be the rotation of point H by angle 3pi/4 around point O. Let G be the reflection of point V across point H. Let J be the reflection of point D across point O. Let E be the rotation of point J by angle 5pi/12 around point V. Let Y be the perpendicular bisector of segment OD. Line Z passes through point V perpendicular to line Y. Point T is the reflection of point G across line Z. Point Q is the reflection of point V across line Y. Line A passes through point O parallel to segment EQ. Point N is the reflection of point T across line A. Find the distance between points N and H. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62.4", "dataset": "MATH"}
{"messages": [{"content": "Let KI = 1. Let V be the rotation of point I by angle pi/2 around point K. Point U is obtained by rotating point V by angle 11pi/12 about point I. Let P be the midpoint of segment KI. Let C be the rotation of point U by angle pi/2 around point P. Point M is the reflection of point U across segment KV. Let O be the reflection of point U across point M. Let Y be the midpoint of segment KV. Let H be the reflection of point Y across point C. Let D be the angle bisector of angle HCV. Line A is the reflection of line D across point U. Point R is the reflection of point Y across line A. Find the distance between points R and O. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.58", "dataset": "MATH"}
{"messages": [{"content": "VT = 12. Point O is the reflection of point T across point V. Let S be the midpoint of segment VO. Point G is obtained by rotating point O by angle 2pi/3 about point S. Let Z be the rotation of point V by angle pi/12 around point S. Let Q be the perpendicular bisector of segment OT. Line H is the angle bisector of angle GZO. Point W is the reflection of point T across line H. Let Y be the reflection of line Q across line H. Point R is the reflection of point O across point W. Point F is the reflection of point R across line Y. Let X be the line through point F perpendicular to segment VZ. Point J is the reflection of point V across line X. What is the distance between points J and S? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56.76", "dataset": "MATH"}
{"messages": [{"content": "TP = 9. Point W is obtained by rotating point P by angle pi/12 about point T. Let F be the midpoint of segment TP. Let V be the angle bisector of angle TWP. Point Z is the reflection of point P across line V. Point G is the reflection of point F across line V. Let U be the midpoint of segment ZG. What is the length of segment UG? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
{"messages": [{"content": "HZ = 10. Let N be the reflection of point H across point Z. Point I is obtained by rotating point H by angle pi/12 about point Z. Point P is obtained by rotating point N by angle pi/12 about point H. Let E be the rotation of point P by angle 11pi/12 around point N. Let C be the rotation of point E by angle 7pi/12 around point P. Line T is the perpendicular bisector of segment IC. Point U is the reflection of point P across line T. Point J is the reflection of point U across segment IC. What is the distance between points J and P? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.32", "dataset": "MATH"}
{"messages": [{"content": "Let HJ = 7. Let C be the midpoint of segment HJ. Let V be the reflection of point C across point J. Line L passes through point C perpendicular to segment HJ. Let W be the rotation of point V by angle pi/12 around point H. Point I is the reflection of point H across point J. Point S is the reflection of point W across segment HJ. Point U is the reflection of point I across line L. Let D be the midpoint of segment US. Point B is obtained by rotating point I by angle pi/6 about point V. Let T be the rotation of point U by angle 3pi/4 around point J. Point M is the midpoint of segment BU. Let X be the angle bisector of angle CIT. Point G is the reflection of point M across segment HJ. Point R is the reflection of point G across line X. Let Z be the reflection of point U across point R. What is the distance between points D and Z? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42.63", "dataset": "MATH"}
{"messages": [{"content": "KR = 6. Let J be the vector from point K to point R. Let U be the rotation of point R by angle 11pi/12 around point K. Point L is obtained by rotating point U by angle pi/4 about point K. Let X be point R translated by vector J. Line Y is the perpendicular bisector of segment LR. Line C passes through point U parallel to line Y. Point B is the reflection of point X across line C. Let E be the midpoint of segment LR. Let W be the reflection of point U across point E. What is the length of segment WB? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.34", "dataset": "MATH"}
{"messages": [{"content": "PX = 4. Let I be the line through points X and P. Line L passes through point X perpendicular to line I. Point G is on line L with |GX| = 2. Point Q is the reflection of point X across point G. Line A is the perpendicular bisector of segment GP. Line Z passes through point G perpendicular to line A. Point B is the reflection of point X across segment PQ. Point U is the reflection of point X across line Z. Find the distance between points B and U. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.53", "dataset": "MATH"}
{"messages": [{"content": "OT = 10. Line E passes through points O and T. Line D is the perpendicular bisector of segment TO. Let A be the reflection of point O across point T. Line B is the reflection of line D across point O. Point F is obtained by rotating point T by angle 5pi/12 about point O. Let X be the reflection of line E through point F. Let Q be the line through point A perpendicular to segment FT. Point I is the reflection of point T across line Q. Point M is the midpoint of segment FT. Point H is obtained by rotating point M by angle 5pi/12 about point I. Let U be the reflection of line X through point H. Point Y is the intersection of lines U and B. Point W is the reflection of point Y across segment AM. Point P is the reflection of point W across segment FT. What is the length of segment PW? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106.29", "dataset": "MATH"}
{"messages": [{"content": "EX = 1. Point G is the reflection of point X across point E. Line H is the perpendicular bisector of segment GX. Point C lies on line H at distance 4 from point G. J is constructed so that CJ = 1. Let D be the angle bisector of angle JXC. Point Q lies on line D at distance 5 from point J. Point R is the reflection of point Q across point X. Let O be the midpoint of segment CR. Point B is the midpoint of segment GR. Find the length of segment BO. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.06", "dataset": "MATH"}
{"messages": [{"content": "CR = 8. Let Y be the line through points C and R. Point B is the reflection of point R across point C. Point U is obtained by rotating point C by angle pi about point R. Point N is obtained by rotating point B by angle pi/6 about point U. Let S be the midpoint of segment BC. Let X be the reflection of point N across point B. Let O be the angle bisector of angle UCN. Let W be the line through point B perpendicular to line O. Line A passes through point X parallel to line W. Point L is the intersection of lines Y and A. Find the distance between points L and S. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.92", "dataset": "MATH"}
{"messages": [{"content": "Let GA = 11. Line U passes through points A and G. Point M is obtained by rotating point A by angle pi/4 about point G. Let H be the midpoint of segment AM. Let B be the line through points M and G. Point Y is the reflection of point H across line U. Point C is the reflection of point H across line B. What is the measure of angle CYH, in radians? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.39", "dataset": "MATH"}
{"messages": [{"content": "Let FT = 1. Line X is the perpendicular bisector of segment TF. Let Y be the reflection of point F across point T. Line D is the reflection of line X across point T. Line M is the perpendicular bisector of segment FY. Let N be the reflection of point Y across point F. Point C is the reflection of point Y across point N. Let G be the reflection of point T across point F. Let H be the angle bisector of angle TFG. Let I be the reflection of line M across line D. Point Q is the reflection of point C across line I. Point U is the reflection of point Q across line H. Find the distance between points U and G. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.0", "dataset": "MATH"}
{"messages": [{"content": "Let KO = 5. Let Z be the line through point O perpendicular to segment KO. Point R lies on line Z at distance 1 from point O. Point L is the reflection of point O across point K. Let A be the midpoint of segment KO. Point I is the reflection of point A across point L. Let G be the midpoint of segment KR. Point W is the reflection of point I across segment KR. Line S passes through points W and I. Point U is the reflection of point G across line S. Let Q be the midpoint of segment UI. Find the length of segment KQ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.7", "dataset": "MATH"}
{"messages": [{"content": "ZY = 8. Let J be the midpoint of segment YZ. Let O be the reflection of point Y across point Z. Let H be the rotation of point O by angle pi/3 around point Z. Let R be the reflection of point J across point Z. Line G is the perpendicular bisector of segment HZ. Line P passes through point R parallel to line G. Point W is the reflection of point H across line P. What is the length of segment HW? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.0", "dataset": "MATH"}